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The number of combinations that can be formed from n different objects taken r at a time is nCr = ____!(n - r)!
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 ____!
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.
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
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)!
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)!
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Number of permutations of n dissimilar things taken r at a time when p particular things always occur = n - pC____ - p x ____!
Number of permutations of n dissimilar things taken r at a time when p particular things always occur = n - pC____ - p x ____!
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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).
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).
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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.
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.
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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.
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.
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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 _______.
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 _______.
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Circular permutations focus on the _______ of an object relative to the others.
Circular permutations focus on the _______ of an object relative to the others.
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In circular permutations, we fix the _______ of one of the objects and then arrange the other objects in all possible ways.
In circular permutations, we fix the _______ of one of the objects and then arrange the other objects in all possible ways.
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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.
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.
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The rule by which any power of binomial expression can be expanded is called the ______ theorem
The rule by which any power of binomial expression can be expanded is called the ______ theorem
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If n is a positive integer and x, y ∈ C then (x + y)^n = ∑ n Cr.x^n − r.y^r where r = ______
If n is a positive integer and x, y ∈ C then (x + y)^n = ∑ n Cr.x^n − r.y^r where r = ______
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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 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 ______
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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 ______
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 ______
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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 ______
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 ______
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For a binomial expression (x + y)^n, nCr is called the ______ coefficients
For a binomial expression (x + y)^n, nCr is called the ______ coefficients
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