Permutation and Combination

(26) In how many ways can you arrange the letters of the word “ELEPHANT”?

• (a) 5040
• (b) 40320
• (c) 362880
• (d) 725760

Answer

Correct Answer: (d) 725760
The number of different ways to arrange the letters of the word “ELEPHANT” is \frac{8!}{2!2!} = 725760 .

(27) A box contains 3 red balls, 4 green balls, and 2 blue balls. In how many ways can you choose 2 balls from the box?

• (a) 36
• (b) 45
• (c) 15
• (d) 18

Answer

Correct Answer: (b) 45
The number of ways to choose 2 balls from the box containing 3 red balls, 4 green balls, and 2 blue balls is ^{9}C_{2} = \frac{9!}{2!(9-2)!} = 45 .

(28) How many different 5-letter words can be formed using the letters of the word “TENNIS”?

• (a) 360
• (b) 120
• (c) 720
• (d) 240

Answer

Correct Answer: (c) 720
The number of different 5-letter words that can be formed using the letters of the word “TENNIS” is \frac{6!}{2!} = 720 .

(29) In how many ways can you arrange the digits 2, 4, 6, 8, 9, and 1 to form a 6-digit number without repetition?

• (a) 720
• (b) 360
• (c) 720
• (d) 1440

Answer

Correct Answer: (c) 720
The number of different 6-digit numbers that can be formed using the digits 2, 4, 6, 8, 9, and 1 without repetition is 6! = 720 .

(30) How many different ways can you choose 4 marbles from a bag containing 7 red marbles and 5 blue marbles?

• (a) 84
• (b) 35
• (c) 462
• (d) 120

Answer

Correct Answer: (c) 462
The number of ways to choose 4 marbles from the bag containing 7 red marbles and 5 blue marbles is ^{12}C_{4} = \frac{12!}{4!(12-4)!} = 462 .