Question

To fill 12 vacancies there are 25 candidates of which five are from scheduled caste. If 3 of the vacancies are reserved for scheduled caste candidates while the rest are open to all, then the number of ways in which the selection can be made

• A. $5C_{3} \times^{22}C_{9}$
• B. $22C_{9} -^{5}C_{3}$
• C. $22C_{3} +^{5}C_{3}$
• D. None of these

Answer 1

Answer: (A)

$5C_{3} \times^{22}C_{9}$

Answer 2

The selection can be made in $5C_{3} \times^{22}C_{9}$ [since 3 vacancies filled from 5 candidates in $5C_{3}$ ways and now remaining candidates are 22 and remaining seats are 9, then remaining vacancies filled by $22C_{9}$ ways. Hence total number of ways $5C_{3} \times^{22}C_{9}$.