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

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

Answer 2

Answer: 363242880

Explanation:

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

`^nC_r=(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=(14!)/((14-4)4!)\\\\=(14*13*12*11*10!)/(10!4!)\\\\=(14*13*12*11)/(4*3*2)=363242880`

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