In how many ways can a committee of 5 be formed from 5 juniors and 7 seniors if the committee must have 3 seniors?

• A. 240

• B. 350

• C. 520

• D. 720

There are 11 different food items in a buffet. A customer is asked to get a certain number of items. If the customer has 462 possible ways as a result, which of the following did he possibly do?

• A. Choose 4 out of the 11 items

• B. Choose 6 out of the 11 items

• C. Choose 7 out of the 11 items

• D. Choose 8 out of the 11 items

44. If a combination lock must contain 5 different digits, in how many ways can a code be formed from the digits 0 to 9?

• A. 15 120

• B. 30 240

• C. 151 200

• D. 1 000 000

Samantha is transferring to a new house. She has a collection of books but she cannot take them all with her. In how many ways can she select 7 books out of 10, and then arrange these books on a shelf if there is space enough for only 5 books?

• A. 3 024

• B. 30 240

• C. 302 400

• D. 3 024 000

The number of permutations of the 4-letter word HOPE taken 2 at a time is 12, find its number of combinations.

• A. 8

• C. 4

• B. 6

• D. 2

Anna, a dress-shop owner has several new dresses to be displayed through her available mannequins. If she can dress these mannequins in 60 different ways, which of the following could be the number of new dresses and mannequins she has?

• A. 3 new dresses, 3 mannequins

• B. 3 new dresses, 4 mannequins

• C. 5 new dresses, 3 mannequins

• D. 5 new dresses, 4 mannequins

Numbers with the same number of digits shall be formed from 2, 4, 5, 7, 8, and 9 such that repetition of digit is not allowed. If 720 numbers can be formed, how many digits do these numbers contain?

• 3

• 4

• 5

• 6

From the situation given, determine if the scenario involves permutation or combination, then find the number of possibilities. There are 9 applicants for three Computer Programmer positions.

• A. Combination; 84

• B. Combination; 504

• C. Permutation; 504

• D. Permutation; 3,024

A girl was invited to a party. She has several available blouses and skirts on her closet. Knowing that any of her blouses can be paired with any of her skirts, she calculated that she could have 42 blouse-skirt pairing to choose to. Which of the following could be the number of blouses and skirts the girl has in her closet?

• A. 6 blouses, 6 skirts

• B. 6 blouses, 7 skirts

• C. 7 blouses, 6 skirts

• D. 7 blouses, 7 skirts

Consider the problem below: How many different ways can 5 books be arranged on a shelf if they can be selected from 7 books? Question: Which of the solutions below would lead to finding the correct permutation of the books?

• A. P(5,5) = 5!

• B. P(7,7) = 7!

• C. P(7,5) = 7.6.5.4.3

• D. P(5,7) = 5.6.7.8.9.10.11