Permutation and Combination Basics

Play an AI-generated podcast conversation about this lesson

The number of combinations that can be formed from n different objects taken r at a time is nCr = ____!(n - r)!

n

The number of permutations of n different things, taken all at a time, out of which p are alike and are of one type, q are alike and are of second type and rest are all different = ! x !

p, q

The number of permutations of n different things taken r at a time when each thing may be repeated any number of times is ____r.

n

Nuber of perutations of n different things, taken all at a tie, when specified things always coe together is ! x (n - __ + 1)!

m Signup and view all the answers

Number of permutations of n dissimilar things taken r at a time when p particular things always occur = n - pC - p x !

r, r Signup and view all the answers

The total number of permutations of n different things taken not more than r at a time, when each thing may be repeated any number of times, is n(n ____ - 1).

r Signup and view all the answers

Number of permutations of n different things, taken all at a time, when m specified things never come together is n !− m !× ( n − m + 1) !. This is an example of a _________ formula.

permutation Signup and view all the answers

Let there be n objects, of which m objects are alike of one kind, and the remaining (n – m) objects are alike of another kind. The total number of mutually distinguishable permutations that can be formed from these objects is ( m !) × ( n − m )! This is an example of a _______ formula.

permutation Signup and view all the answers

If there are n objects, of which p1 are alike of one kind; p2 are alike of another kind; p3 are alike of 3rd kind; ….; pr are alike of rth kind such that p1 + p2 +....+ pr = n; then the number of permutations of these n objects is ( p1 !) × ( p2 !) ×....× ( pr !). This formula is related to _______.

permutation Signup and view all the answers

Circular permutations focus on the _______ of an object relative to the others.

position Signup and view all the answers

In circular permutations, we fix the _______ of one of the objects and then arrange the other objects in all possible ways.

position Signup and view all the answers

There are two types of circular permutations: one where clockwise and anticlockwise arrangements give rise to different permutations and the other where clockwise and anticlockwise arrangements give rise to the same permutations. These are examples of _______ permutations.

circular Signup and view all the answers

The rule by which any power of binomial expression can be expanded is called the ______ theorem

binomial Signup and view all the answers

If n is a positive integer and x, y ∈ C then (x + y)^n = ∑ n Cr.x^n − r.y^r where r = ______

0 Signup and view all the answers

Replacing y by −y in the binomial expansion, we get (x - y)^n = ∑ (−1)^nCr.x^n − r.y^r where the terms are alternatively and

positive, negative Signup and view all the answers

Replacing x by 1 and y by x in the binomial expansion equation, we get (1 + x)^n = ∑ nCr*x^r where r ranges from to

0, n Signup and view all the answers

The expansion of (1 - x)^n by replacing x with 1 and y with -x is (1 - x)^n = ∑ (−1)^rnCrx^r where r ranges from to

0, n Signup and view all the answers

For a binomial expression (x + y)^n, nCr is called the ______ coefficients

binomial Signup and view all the answers

Permutation and Combination Basics

Podcast Beta

Questions and Answers

The number of combinations that can be formed from n different objects taken r at a time is nCr = ____!(n - r)!

The number of permutations of n different things, taken all at a time, out of which p are alike and are of one type, q are alike and are of second type and rest are all different = ! x !

The number of permutations of n different things taken r at a time when each thing may be repeated any number of times is ____r.

Nuber of perutations of n different things, taken all at a tie, when specified things always coe together is ! x (n - __ + 1)!

Number of permutations of n dissimilar things taken r at a time when p particular things always occur = n - pC - p x !

The total number of permutations of n different things taken not more than r at a time, when each thing may be repeated any number of times, is n(n ____ - 1).

Number of permutations of n different things, taken all at a time, when m specified things never come together is n !− m !× ( n − m + 1) !. This is an example of a _________ formula.

Let there be n objects, of which m objects are alike of one kind, and the remaining (n – m) objects are alike of another kind. The total number of mutually distinguishable permutations that can be formed from these objects is ( m !) × ( n − m )! This is an example of a _______ formula.

Circular permutations focus on the _______ of an object relative to the others.

In circular permutations, we fix the _______ of one of the objects and then arrange the other objects in all possible ways.

There are two types of circular permutations: one where clockwise and anticlockwise arrangements give rise to different permutations and the other where clockwise and anticlockwise arrangements give rise to the same permutations. These are examples of _______ permutations.

The rule by which any power of binomial expression can be expanded is called the ______ theorem

If n is a positive integer and x, y ∈ C then (x + y)^n = ∑ n Cr.x^n − r.y^r where r = ______

Replacing y by −y in the binomial expansion, we get (x - y)^n = ∑ (−1)^nCr.x^n − r.y^r where the terms are alternatively and

Replacing x by 1 and y by x in the binomial expansion equation, we get (1 + x)^n = ∑ nCr*x^r where r ranges from to

The expansion of (1 - x)^n by replacing x with 1 and y with -x is (1 - x)^n = ∑ (−1)^rnCrx^r where r ranges from to

For a binomial expression (x + y)^n, nCr is called the ______ coefficients

More Quizzes Like This

Permutation vs Combination

Permutation and Combination Quiz with Answers

Quiz on Defectives per 1000 Items - Engineering Mathematics Vol 1 Set...

Permutation and Combination Basics

Upgrade to continue

Permutation and Combination Basics

Podcast Beta

Questions and Answers

The number of combinations that can be formed from n different objects taken r at a time is nCr = ____!(n - r)!

The number of permutations of n different things, taken all at a time, out of which p are alike and are of one type, q are alike and are of second type and rest are all different = ____! x ____!

The number of permutations of n different things taken r at a time when each thing may be repeated any number of times is ____r.

Nu______ber of per______utations of n different things, taken all at a ti______e, when ______ specified things always co______e together is ______! x (n - ______ + 1)!

Number of permutations of n dissimilar things taken r at a time when p particular things always occur = n - pC____ - p x ____!

The total number of permutations of n different things taken not more than r at a time, when each thing may be repeated any number of times, is n(n ____ - 1).

Number of permutations of n different things, taken all at a time, when m specified things never come together is n !− m !× ( n − m + 1) !. This is an example of a _________ formula.

Let there be n objects, of which m objects are alike of one kind, and the remaining (n – m) objects are alike of another kind. The total number of mutually distinguishable permutations that can be formed from these objects is ( m !) × ( n − m )! This is an example of a _______ formula.

Circular permutations focus on the _______ of an object relative to the others.

In circular permutations, we fix the _______ of one of the objects and then arrange the other objects in all possible ways.

There are two types of circular permutations: one where clockwise and anticlockwise arrangements give rise to different permutations and the other where clockwise and anticlockwise arrangements give rise to the same permutations. These are examples of _______ permutations.

The rule by which any power of binomial expression can be expanded is called the ______ theorem

If n is a positive integer and x, y ∈ C then (x + y)^n = ∑ n Cr.x^n − r.y^r where r = ______

Replacing y by −y in the binomial expansion, we get (x - y)^n = ∑ (−1)^nCr.x^n − r.y^r where the terms are alternatively ______ and ______

Replacing x by 1 and y by x in the binomial expansion equation, we get (1 + x)^n = ∑ nCr*x^r where r ranges from ______ to ______

The expansion of (1 - x)^n by replacing x with 1 and y with -x is (1 - x)^n = ∑ (−1)^rnCrx^r where r ranges from ______ to ______

For a binomial expression (x + y)^n, nCr is called the ______ coefficients

More Quizzes Like This

Permutation vs Combination

Permutation and Combination Quiz with Answers

Quiz on Defectives per 1000 Items - Engineering Mathematics Vol 1 Set...

Permutation and Combination Basics

The number of permutations of n different things, taken all at a time, out of which p are alike and are of one type, q are alike and are of second type and rest are all different = ! x !

Nuber of perutations of n different things, taken all at a tie, when specified things always coe together is ! x (n - __ + 1)!

Number of permutations of n dissimilar things taken r at a time when p particular things always occur = n - pC - p x !

Replacing y by −y in the binomial expansion, we get (x - y)^n = ∑ (−1)^nCr.x^n − r.y^r where the terms are alternatively and

Replacing x by 1 and y by x in the binomial expansion equation, we get (1 + x)^n = ∑ nCr*x^r where r ranges from to

The expansion of (1 - x)^n by replacing x with 1 and y with -x is (1 - x)^n = ∑ (−1)^rnCrx^r where r ranges from to