Permutation and Combination

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

• (a) 15120
• (b) 10080
• (c) 720
• (d) 5040

Answer

Correct Answer: (b) 10080
The number of different ways to arrange the letters of the word “PARALLEL” is \frac{8!}{3!2!} = 10080 .

(67) A box contains 7 red balls, 6 green balls, and 5 blue balls. In how many ways can you choose 7 balls from the box?

• (a) 34650
• (b) 18564
• (c) 135135
• (d) 28028

Answer

Correct Answer: (c) 135135
The number of ways to choose 7 balls from the box containing 7 red balls, 6 green balls, and 5 blue balls is ^{18}C_{7} = \frac{18!}{7!(18-7)!} = 135135 .

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

• (a) 720
• (b) 120
• (c) 3600
• (d) 1440

Answer

Correct Answer: (c) 3600
The number of different 5-letter words that can be formed using the letters of the word “EXOTIC” is \frac{6!}{2!} = 3600 .

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

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

Answer

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

(70) How many different ways can you choose 6 marbles from a bag containing 16 red marbles and 11 blue marbles?

• (a) 12376
• (b) 38760
• (c) 12376
• (d) 61880

Answer

Correct Answer: (c) 12376
The number of ways to choose 6 marbles from the bag containing 16 red marbles and 11 blue marbles is ^{27}C_{6} = \frac{27!}{6!(27-6)!} = 12376 .