AAPL wrote:Veritas Prep

On her way home from a business trip, Janice remembers that she needs to buy each of her three children a souvenir. At the airport shop, the only items there left are two hats, two t-shirts, two posters, and two keychains. How many combinations can she select from if she wants each child to receive a different item?

A. 24
B. 32
C. 40
D. 48
E. 56

OA B

So Jenice is to choose 3 items out of 2 hats, 2 t-shirts, 2 posters, and 2 keychains given that she wants each child to receive a different item.

Say she chooses 1 item each out of 2 hats, 2 t-shirts, and 2 posters. The number of ways she can do choose = 2*2*2 = 8;

The number of ways she can choose any 3 categories of items to choose one item each from them = 4C3 = 4C1 = 4

Thus, the total number of ways = 8*4 =32

The correct answer: B

Hope this helps!

-Jay
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AAPL wrote:Veritas Prep

On her way home from a business trip, Janice remembers that she needs to buy each of her three children a souvenir. At the airport shop, the only items there left are two hats, two t-shirts, two posters, and two keychains. How many combinations can she select from if she wants each child to receive a different item?

A. 24
B. 32
C. 40
D. 48
E. 56

OA B

She has 4C3 = 4 choices to choose 3 items out 4 unique items (hat, t-shirt, poster, and keychain). Since each unique item has 2 choices, she has 2 x 2 x 2 = 8 ways to choose any group of 3 unique items. Therefore, she has a total of 4 x 8 = 32 ways to choose 3 unique items for her 3 children.

Answer: B