Question

Скількома способами можна вибрати при з 11-ти різних новорічних подарункових набори?​

Answer 1

$C_{11}^3 = \dfrac{11!}{3!(11-3)!} = \dfrac{11!}{3!8!} = \dfrac{9\cdot10\cdot11}{2\cdot3} = 165$

Answer 2

Calculation of the Number of Ways to Choose New Year's Gift Sets

To calculate the number of ways to choose from 11 different New Year's gift sets, we can use the concept of combinations.

The formula for calculating combinations is:

C(n, r) = n! / (r! * (n-r)!)

Where: - n is the total number of items to choose from - r is the number of items to be chosen - ! denotes the factorial operation

In this case, we have 11 different gift sets, and we want to choose all of them. So, we need to calculate C(11, 11).

Using the formula, we can calculate the number of ways as follows:

C(11, 11) = 11! / (11! * (11-11)!) = 11! / (11! * 0!) = 1

Therefore, there is only 1 way to choose all 11 different New Year's gift sets.

Please note that this calculation assumes that each gift set is distinct and cannot be repeated.