Question

A student is to answer 10 out of 13 questions in an examination such that he must choose at least 4 from the first five questions. The number of choices available to him is

• A. 140
• B. 196
• C. 280
• D. 346

Answer 1

Answer: (B)

196

There would be two cases,

(1) When 4 is selected from first five and rest 6 from remaining 8.

This is done in ${}^5{C}_4{\times }^8{C}_6$ ways.

(2) When all 5 are selected from first five and rest five from remaining 8.

This can be done in ${}^5{C}_5{\times }^8{C}_5$ ways.

$\therefore$ A total of ${}^5{C}_4{\times }^8{C}_6{+}^5{C}_5{\times }^8{C}_5$

$=5\times \frac{8!}{6!2!}+\frac{8!}{3!5!}$

$=\frac{5\times 8\times 7}{2}+\frac{8\times 7\times 8}{3\times 2}$

$=140+56=196ways$