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

455 ways

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 = (n!)/((n - r)!r!)`

So, we have:

`^(15)C_3 = (15!)/((15 - 3)!3!)`

`^(15)C_3 = (15!)/(12!*3!)`

Expand

`^(15)C_3 = (15*14*13*12!)/(12!*3*2*1)`

`^(15)C_3 = (15*14*13)/(3*2*1)`

`^(15)C_3 = (2730)/(6)`

`^(15)C_3 = 455`