Permutation and Combination

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

• (a) 30240
• (b) 15120
• (c) 166320
• (d) 997920

Answer

Correct Answer: (c) 166320
The number of different ways to arrange the letters of the word “OCCURRENCE” is \frac{11!}{2!2!2!} = 166320 .

(57) A box contains 8 red balls, 5 green balls, and 4 blue balls. In how many ways can you choose 6 balls from the box?

• (a) 4005
• (b) 36960
• (c) 42504
• (d) 29700

Answer

Correct Answer: (c) 42504
The number of ways to choose 6 balls from the box containing 8 red balls, 5 green balls, and 4 blue balls is ^{17}C_{6} = \frac{17!}{6!(17-6)!} = 42504 .

(58) How many different 7-letter words can be formed using the letters of the word “COMPUTER”?

• (a) 5040
• (b) 20160
• (c) 50400
• (d) 10080

Answer

Correct Answer: (c) 50400
The number of different 7-letter words that can be formed using the letters of the word “COMPUTER” is \frac{8!}{2!} = 50400 .

(59) In how many ways can you arrange the digits 1, 2, 3, 4, 5, 6, 7, 8, 9, and 0 to form a 10-digit number without repetition?

• (a) 362880
• (b) 40320
• (c) 3628800
• (d) 403200

Answer

Correct Answer: (c) 3628800
The number of different 10-digit numbers that can be formed using the digits 1, 2, 3, 4, 5, 6, 7, 8, 9, and 0 without repetition is 10! = 3628800 .

(60) How many different ways can you choose 7 marbles from a bag containing 18 red marbles and 12 blue marbles?

• (a) 18144
• (b) 27588
• (c) 31824
• (d) 22680

Answer

Correct Answer: (c) 31824
The number of ways to choose 7 marbles from the bag containing 18 red marbles and 12 blue marbles is ^{30}C_{7} = \frac{30!}{7!(30-7)!} = 31824 .