Answer: 363242880
Step-by-step explanation:
We know that the of to calculate the number of combinations, we use the formula :-
[tex]^nC_r=\dfrac{n!}{r!(n-r)!}[/tex], 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 :-
[tex]^{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[/tex]
Hence, If 4 scarves are picked randomly from the box, 363242880 different combinations are possible if the order doesn't matter.
