Permutation and Combination

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

• (a) 40320
• (b) 10080
• (c) 725760
• (d) 1440

Answer

Correct Answer: (b) 10080
The number of different ways to arrange the letters of the word “COMPUTER” is \frac{8!}{2!2!} = 10080 .

(32) A box contains 5 red balls, 3 green balls, and 4 blue balls. In how many ways can you choose 3 balls from the box?

• (a) 84
• (b) 165
• (c) 220
• (d) 330

Answer

Correct Answer: (c) 220
The number of ways to choose 3 balls from the box containing 5 red balls, 3 green balls, and 4 blue balls is ^{12}C_{3} = \frac{12!}{3!(12-3)!} = 220 .

(33) How many different 6-letter words can be formed using the letters of the word “SEQUENCE”?

• (a) 1440
• (b) 360
• (c) 4320
• (d) 720

Answer

Correct Answer: (c) 4320
The number of different 6-letter words that can be formed using the letters of the word “SEQUENCE” is \frac{8!}{2!} = 4320 .

(34) In how many ways can you arrange the digits 3, 5, 7, 9, 1, and 2 to form a 6-digit number without repetition?

• (a) 720
• (b) 120
• (c) 720
• (d) 1440

Answer

Correct Answer: (c) 720
The number of different 6-digit numbers that can be formed using the digits 3, 5, 7, 9, 1, and 2 without repetition is 6! = 720 .

(35) How many different ways can you choose 2 marbles from a bag containing 8 red marbles and 6 blue marbles?

• (a) 112
• (b) 336
• (c) 84
• (d) 168

Answer

Correct Answer: (c) 84
The number of ways to choose 2 marbles from the bag containing 8 red marbles and 6 blue marbles is ^{14}C_{2} = \frac{14!}{2!(14-2)!} = 84 .