Question

Consider a bag containing five red marbles, two green ones, one transparent one, four yellow ones, and two orange ones How many possible sets of five marbles are there in which none of them are red or green? sets Need Help? Tente Tutor

Answer 1

Answer:  21

Step-by-step explanation:

Given : A contains five red marbles, two green ones, one transparent one, four yellow ones, and two orange ones.

Total marbles = $5+2+1+4+2=14$

Number of marbles except red or green =14-5-2=7

∵ Combinations of n things taken m at a time is given by :-

$^nC_m=\dfrac{n!}{m!(n-m)!}$

Now, the number of  possible sets of five marbles are there in which none of them are red or green :_

$^7C_5=\dfrac{7!}{(7-5)!5!}\\\\=\dfrac{7\times6\times5!}{2\times5!}=21$

Hence, the number of  possible sets of five marbles are there in which none of them are red or green=21