Question

You want to send postcards to 15 friends. In the shop there are only 3 kinds of postcards. In how many ways can you send the postcards, if

Answer 1

Answer:

455 ways

Step-by-step explanation:

Given

$n = 15$ --- friends

$r = 3$ -- available postcard kinds

Required

Ways of sending the cards

The question is an illustration of combination and the formula is:

$^nC_r = \frac{n!}{(n - r)!r!}$

So, we have:

$^{15}C_3 = \frac{15!}{(15 - 3)!3!}$

$^{15}C_3 = \frac{15!}{12!*3!}$

Expand

$^{15}C_3 = \frac{15*14*13*12!}{12!*3*2*1}$

$^{15}C_3 = \frac{15*14*13}{3*2*1}$

$^{15}C_3 = \frac{2730}{6}$

$^{15}C_3 = 455$