Question

Kelsey is writing a thank-you note to a friend. She has 9 kinds of cards and 7 kinds of envelopes that fit the cards. She has 3 designs of first-class stamps, although she only needs to use one. Finally, Kelsey has to pick a color of pen with which to write the note, and she has 2 to choose from. How many different ways can the thank-you note look?

Answer 1

378

Explanation:

Work 1:

She has 9 kinds of cards out of which she has to chose only 1.

The number of ways of doing this is 9 (she can pick any one of them).

Work 2:

She has 7 kinds of cards out of which she has to chose only 1.

The number of ways of doing this is 7 (she can pick any one of them).

Work 3:

She has 3 designs of first-class stamps out of which she has to chose only 1.

The number of ways of doing this is 3 (she can pick any one of them).

Work 4:

She has to pick the color of pen and she has 2 to choose from.

The number of ways of doing this is 2 (she can choose any one of them).

She has to do Work 1 and Work 2 and Work 3 and Work 4.

∴By the fundamental counting principle, the total number of different ways in which the thank-you note can look is 9×7×3×2 = 378