A game has a deck of cards that are colored red, blue, yellow, and green. Shawn has 5 cards in his hand. If Shawn’s cards are only blue and yellow, how many different combinations of blue and yellow cards could he have?

Fawzia,

The simplest approach is to think about what Shawn's hand can look like if he has only blue and yellow cards and five cards in his hand.

He can have

0 blue and 5 yellow

1 blue and 4 yellow

2 blue and 3 yellow

3 blue and 2 yellow

4 blue and 1 yellow

5 blue and 0 yellow

Or six combinations of blue and yellow cards. This analysis assumes that the blue cards are indistinguishable from each other and that the yellow cards are similarly indistinguishable from each other. If the cards were numbered (like a traditional deck
of cards), we could distinguish among more combinations of blue and yellow cards.

I hope this helps. John