Question

A swimming team has eight members, only two of which are boys. The coach wants to take a delegation from the team to a special swimming camp. If the delegation must have either five or six members, and must include atleast one boy, then the number of ways to select the delegation, is

• A. 66
• B. 77
• C. 88
• D. 99

Answer 1

Answer: (B)

METHOD - 1
CASE - 1 : Delegation consists of $5$ members
(a) $1$ Boy $+4$ Girls ${}^2{C}_1\times {}^6{C}_4=30$
(b) $2$ Boys $+3$ Girls ${}^2{C}_2\times {}^6{C}_3=20$
$50$
CASE - 2 : Delegation consists of $6$ members
(a) $1$ Boy $+5$ Girls ${}^2{C}_1\times {}^6{C}_5=12$
(b) $2$ Boys $+4$ Girls $2C2\times {}^6{C}_4=15$
$77$ ways
METHOD-2
CASE - 1 : Delegation consists of $5$ members
Total number of ways of selecting $5$ member team number of ways when no boy is selected
$={}^8{C}_5-{}^6{C}_5=50$
CASE - 2 : Delegation consists of 6 members
$\therefore$ Total - no, boy is selected
$={}^8{C}_6-{}^6{C}_6=27$
Total $=50+27=77$