Permutation and Combination

(16) How many different ways can you arrange the letters of the word “SUCCESS”?

• (a) 1260
• (b) 2520
• (c) 5040
• (d) 1512

Answer

Correct Answer: (b) 2520
The number of different ways to arrange the letters of the word “SUCCESS” is \frac{7!}{2!2!2!} = 2520 , where we divide by the factorial of the number of times each letter repeats.

(17) In how many ways can you choose a committee of 3 students from a class of 10 students?

• (a) 10
• (b) 30
• (c) 120
• (d) 720

Answer

Correct Answer: (c) 120
The number of ways to choose a committee of 3 students from a class of 10 students is ^{10}C_{3} = \frac{10!}{3!(10-3)!} = 120 .

(18) In how many ways can you arrange the digits 1, 2, 3, 4, 5, 6, 7, and 8 to form an 8-digit number, with no digit repeated?

• (a) 40
• (b) 5760
• (c) 40320
• (d) 4032

Answer

Correct Answer: (c) 40320
The number of ways to arrange the digits 1 to 8 without repetition is 8! = 40320 .

(19) A deck of cards contains 52 cards. In how many ways can you choose 5 cards from the deck?

• (a) 259,860
• (b) 2,598,960
• (c) 10,626
• (d) 52,960

Answer

Correct Answer: (b) 2,598,960
The number of ways to choose 5 cards from a deck of 52 cards is ^{52}C_{5} = \frac{52!}{5!(52-5)!} = 2,598,960 .

(20) How many different ways can you arrange the letters of the word “MISSISSIPPI”?

• (a) 34650
• (b) 34650
• (c) 933120
• (d) 140

Answer

Correct Answer: (b) 34650
The number of different ways to arrange the letters of the word “MISSISSIPPI” is \frac{11!}{4!4!2!1!} = 34650 .