27 Questions
What is the formula for the number of permutations of n objects taken r at a time?
n! / (n + r)!
In how many ways can 4 speakers be arranged in a row for a photo?
4 × 3 × 2 × 1!
How many ways can 5 boys and 4 girls be arranged on a bench if boys and girls are in separate groups?
5! × 4! × 2!
How many ways can 5 boys and 4 girls be arranged on a bench if Anne and Jim wish to stay together?
2 × 8!
What is the number of ways to arrange 5 objects in a circle?
(5-1)!
How many 4-digit numbers greater than 4000 can be formed from the digits 2, 3, 4, 5, and 6?
3P1 × 4P3
What is the number of ways 6 men and 6 women can sit at a round table if men and women alternate?
5! × 6!
How many 4-digit even numbers can be formed from the digits 2, 3, 4, 5, and 6?
4P3 × 3P1
What is the number of ways 6 men and 6 women can sit at a round table if there are no restrictions?
11!
How many 5-digit numbers greater than 4000 can be formed from the digits 2, 3, 4, 5, and 6?
5P5
What is the total possible number of hands in a poker game where 5 cards are dealt from a regular pack of 52 cards?
52C5
How many hands of poker have 4 Kings?
C4 × 48C1
How many ways can 4 Maths books be arranged from 6 different Maths books?
6P4
What is the number of ways to choose 3 Aces and 2 Kings from a deck of 52 cards?
C3 × 4C2
What is the number of ways to arrange 7 books on a shelf where 4 Maths books are chosen from 6 different Maths books and 3 English books are chosen from 5 different English books, with no restrictions?
6C4 × 5C3 × 7!
If a bookshelf has 8 shelves and each shelf can hold 5 books, how many ways can the books be arranged on the shelves?
5 × 5 × 5 × 5 × 5 × 5 × 5 × 5
A die is rolled 4 times. What is the number of possible outcomes?
6^4
A license plate consists of 3 letters and 2 digits. How many possible license plates are there?
26 × 26 × 26 × 10 × 10
If 5 people are to be arranged in a row, what is the number of possible arrangements?
5 × 4 × 3 × 2 × 1
If a bag contains 6 balls and 3 balls are drawn at random, what is the number of possible outcomes?
6 × 5 × 4
If a word consists of 4 letters and each letter can be chosen from 26 possible letters, what is the number of possible words?
26 × 26 × 26 × 26
If 4 Maths books are selected from 6 different Maths books and 3 English books are chosen from 5 different English books, how many ways can the seven books be arranged on a shelf if a Maths book is at the beginning of the shelf?
6 × 5C3 × 5C3 × 6!
If 4 Maths books are selected from 6 different Maths books and 3 English books are chosen from 5 different English books, how many ways can the seven books be arranged on a shelf if Maths and English books alternate?
6P4 × 5P3
If 4 Maths books are selected from 6 different Maths books and 3 English books are chosen from 5 different English books, how many ways can the seven books be arranged on a shelf if a Maths book is at the beginning and an English book is in the middle of the shelf?
6 × 5 × 5C3 × 4C2 × 5!
How many different 8 letter words are possible using the letters of the word SYLLABUS?
10 080
If a word is chosen at random from the letters of the word SYLLABUS, what is the probability that the word contains the two S’s together?
2520 / 10 080
What is the formula to find the number of ways to arrange the seven books on a shelf if a Maths book is at the beginning of the shelf?
6 × 5C3 × 5C3 × 6!
Test your understanding of the multiplication rule and repetition of events in permutations and combinations. This quiz is designed for HSC mathematics students revising for their exams.
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