Permutation and Combination

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

• (a) 5040
• (b) 1440
• (c) 10080
• (d) 720

Answer

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

(42) A box contains 7 red balls, 4 green balls, and 3 blue balls. In how many ways can you choose 5 balls from the box?

• (a) 792
• (b) 210
• (c) 1344
• (d) 462

Answer

Correct Answer: (c) 1344
The number of ways to choose 5 balls from the box containing 7 red balls, 4 green balls, and 3 blue balls is ^{14}C_{5} = \frac{14!}{5!(14-5)!} = 1344 .

(43) How many different 8-letter words can be formed using the letters of the word “EXEMPLARY”?

• (a) 362880
• (b) 80640
• (c) 725760
• (d) 14400

Answer

Correct Answer: (c) 725760
The number of different 8-letter words that can be formed using the letters of the word “EXEMPLARY” is \frac{9!}{2!2!} = 725760 .

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

• (a) 40320
• (b) 5760
• (c) 40320
• (d) 10080

Answer

Correct Answer: (c) 40320
The number of different 8-digit numbers that can be formed using the digits 1, 2, 3, 4, 5, 6, 7, and 8 without repetition is 8! = 40320 .

(45) How many different ways can you choose 6 marbles from a bag containing 10 red marbles and 8 blue marbles?

• (a) 210
• (b) 360
• (c) 18564
• (d) 1260

Answer

Correct Answer: (c) 18564
The number of ways to choose 6 marbles from the bag containing 10 red marbles and 8 blue marbles is ^{18}C_{6} = \frac{18!}{6!(18-6)!} = 18564 .