Question

A box contains 14 scarves in unique colors. If 4 scarves are picked randomly from the box,__________ different combinations are possible if the order doesn't matter.

Answer 1

Answer: 363242880

Step-by-step explanation:

We know that the of to calculate the number of combinations, we use the formula :-

$^nC_r=\dfrac{n!}{r!(n-r)!}$, where n : the total number of items

r: the number of items being chosen at a time.

Given: The total number of scarves contained in a box= 14

The number of scarves picked = 4

The number of different combinations is given by :-

$^{14}C_4=\dfrac{14!}{(14-4)4!}\\\\=\dfrac{14\times13\times12\times11\times10!}{10!4!}\\\\=\dfrac{14\times13\times12\times11}{4\times3\times2}=363242880$

Hence,  If 4 scarves are picked randomly from the box, 363242880 different combinations are possible if the order doesn't matter.

Answer 2

This would be 14C4   = (14*13*12*11) / (4*3*2*1)  =   1001