Question

If the selection is to consist of either all males or all females then the number of ways of selecting $10$ clerks from $22$ males and $17$ female applicants is

• A. ${}^{22}{C}_{10}$
• B. ${}^{17}{C}_{10}$
• C. ${}^{22}{C}_{10}$ + ${}^{17}{C}_{10}$
• D. ${}^{20}{C}_3$

Answer 1

The correct option is C ${}^{22}{C}_{10}$ + ${}^{17}{C}_{10}$

$10$ clerks are to be selected from $22$ males and $17$ females.

If all $10$ clerks are men, then the number of ways is

${}^{22}{C}_{10}$

Or if all $10$ clerks are females, then number of ways is

${}^{17}{C}_{10}$

$\therefore$ the total number of ways of selecting $10$ clerks either men or female is

${=}^{22}{C}_{10}{+}^{17}{C}_{10}$

Hence, the answer is option C.