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.

Question

asked May 14, 2018 66.7k views

2 Answers

Stefo · Answer 1 · 2018-05-19T08:17:28+0000

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.