QUIZ 1- PERMUTATIONS

What is the value of 5! ?

• 120

• 150

• 200

• 100

Answer explanation

The value of 5! (5 factorial) is calculated as 5 × 4 × 3 × 2 × 1, which equals 120. Therefore, the correct answer is 120.

Calculate 7! / 5!

• 42

• 50

• 60

• 35

Answer explanation

To calculate 7! / 5!, we simplify: 7! = 7 × 6 × 5!; thus, 7! / 5! = 7 × 6 = 42. Therefore, the correct answer is 42.

What is the formula for permutations of n items taken r at a time?

• n! / (n - r)!

• n! + r!

• n! * (n - r)

• (n + r)! / n!

Answer explanation

The formula for permutations of n items taken r at a time is n! / (n - r)!. This represents the number of ways to arrange r items from a total of n, making the first choice from n, the second from (n-1), and so on.

How many different ways can the letters in the word 'MATH' be arranged?

• 12

• 18

• 24

• 30

Answer explanation

The word 'MATH' has 4 distinct letters. The number of arrangements is calculated using the factorial of the number of letters: 4! = 4 × 3 × 2 × 1 = 24. Therefore, the correct answer is 24.

If you have 4 different books, how many ways can you arrange them on a shelf?

• 12

• 16

• 24

• 30

Answer explanation

To arrange 4 different books, use the factorial of the number of books: 4! = 4 × 3 × 2 × 1 = 24. Thus, there are 24 ways to arrange the books on a shelf, making the correct answer 24.

What is 0! equal to?

• -1

• 1

• 1.5

• 0

Answer explanation

0! is defined as 1 in mathematics. This is a convention that helps in combinatorial calculations and ensures consistency in formulas involving factorials. Therefore, the correct answer is 1.

How many ways can you select 2 toppings from 5 available toppings?

• 20

• 5

• 10

• 15

Answer explanation

To select 2 toppings from 5, use the combination formula C(n, k) = n! / (k!(n-k)!). Here, n=5 and k=2. Thus, C(5, 2) = 5! / (2!3!) = (5×4)/(2×1) = 10. Therefore, the correct answer is 10.

Calculate the number of permutations of the letters in the word 'BOOK'.

• 24

• 12

• 8

• 16

Answer explanation

The word 'BOOK' has 4 letters, with 'O' repeated twice. The formula for permutations of letters with repetitions is n! / (p1! * p2!), where n is the total letters and p1, p2 are the counts of repeated letters. Thus, 4! / (2!) = 12.

If you have 6 different colored balls, how many ways can you choose 2?

• 15

• 20

• 10

• 12

Answer explanation

To choose 2 balls from 6, use the combination formula C(n, k) = n! / (k!(n-k)!). Here, n=6 and k=2. So, C(6, 2) = 6! / (2!(6-2)!) = 15. Thus, the correct answer is 15.

What is the number of ways to arrange 5 books on a shelf if 2 are identical?

• 30

• 120

• 60

• 45

Answer explanation

To arrange 5 books where 2 are identical, use the formula for permutations of multiset: 5! / 2! = 120 / 2 = 60. Thus, the number of ways to arrange the books is 60.