Question

A committee of 11 members is to be formed out of 8 males and 5 females. If m is the number of ways the committee is formed with atleast 6 males and n is the number of ways with atleast 3 females, then

• A. $n=m-8$
• B. $m=n=78$
• C. $m=n=68$
• D. $m+n=68$

Answer 1

The correct option is B $m=n=78$

No. of males =8
No. of females =5
So, atleast 6 males and 3 females will be selected in every possible combination in selection of 11 members out of 8 males and 5 females.
$\therefore m=n={}^{13}{C}_2=\frac{13\times 12}{2}=78.$