Permutation and Combination

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

• (a) 181440
• (b) 30240
• (c) 6048
• (d) 1440

Answer

Correct Answer: (b) 30240
The number of different ways to arrange the letters of the word “TRIANGLE” is \frac{8!}{2!2!} = 30240 .

(22) A club has 6 members. In how many ways can you choose a president, vice president, and secretary from the members?

• (a) 12
• (b) 120
• (c) 720
• (d) 210

Answer

Correct Answer: (b) 120
The number of ways to choose a president, vice president, and secretary from 6 members is ^{6}P_{3} = \frac{6!}{(6-3)!} = 120 .

(23) How many different 4-digit numbers can be formed using the digits 1, 2, 3, and 4 without repetition?

• (a) 16
• (b) 12
• (c) 24
• (d) 8

Answer

Correct Answer: (c) 24
The number of different 4-digit numbers that can be formed using the digits 1, 2, 3, and 4 without repetition is ^{4}P_{4} = 4! = 24 .

(24) In how many ways can you choose 2 red balls, 3 green balls, and 4 blue balls from a bag containing 5 red balls, 6 green balls, and 7 blue balls?

• (a) 420
• (b) 720
• (c) 1260
• (d) 210

Answer

Correct Answer: (c) 1260
The number of ways to choose 2 red balls, 3 green balls, and 4 blue balls from the given bag is ^{5}C_{2} \times ^{6}C_{3} \times ^{7}C_{4} = \frac{5!}{2!(5-2)!} \times \frac{6!}{3!(6-3)!} \times \frac{7!}{4!(7-4)!} = 1260 .

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

• (a) 24
• (b) 120
• (c) 720
• (d) 5040

Answer

Correct Answer: (c) 720
The number of different ways to arrange the letters of the word “APPLE” is \frac{5!}{2!} = 720 .