Q55 / 160 · AP EAMCET 2024 (21 May Shift 1) · Mathematics
The number of ways in which 3 men and 3 women can be arranged in a row of 6 seats, such that the first and last seats must be filled by men is
- A720
- B36
- Correct answerC144
- D72
Solution
$3 \mathrm{M}, 3 \mathrm{~W}$
\begin{array}{|l|l|l|l|l|l|}\hline M & & & & & M \\\hline\end{array}
Number of ways of filling first and last seats $={ }^3 C_2 \times 2!=6$ No. of ways of filling middle seats is $=4$ ! Requires number $=24 \times 6=144$
Number of ways of filling first and last seats $={ }^3 C_2 \times 2!=6$ No. of ways of filling middle seats is $=4$ ! Requires number $=24 \times 6=144$
Hence, the correct answer is option: 'C'.