Permutation and Combination

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

• (a) 34650
• (b) 3465
• (c) 34650
• (d) 69300

Answer

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

(72) A box contains 5 red balls, 3 green balls, and 2 blue balls. In how many ways can you choose 6 balls from the box?

• (a) 210
• (b) 1260
• (c) 3150
• (d) 630

Answer

Correct Answer: (c) 3150
The number of ways to choose 6 balls from the box containing 5 red balls, 3 green balls, and 2 blue balls is ^{10}C_{6} = \frac{10!}{6!(10-6)!} = 3150 .

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

• (a) 10080
• (b) 30240
• (c) 725760
• (d) 40320

Answer

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

(74) 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) 3628800
• (b) 725760
• (c) 36288000
• (d) 7257600

Answer

Correct Answer: (c) 36288000
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! = 36288000 .

(75) How many different ways can you choose 5 marbles from a bag containing 12 red marbles and 8 blue marbles?

• (a) 61880
• (b) 1287
• (c) 792
• (d) 1716

Answer

Correct Answer: (c) 792
The number of ways to choose 5 marbles from the bag containing 12 red marbles and 8 blue marbles is ^{20}C_{5} = \frac{20!}{5!(20-5)!} = 792 .