Five students are selected from 11. How many ways can these stude… - Vidyadip

Question

Five students are selected from 11. How many ways can these students be selected if: two specified students are selected?

✓

Answer

5 students are to be selected from 11 students
(i) When 2 specified students are included
then remaining 3 students can be selected from $(11-2)=9$ students.
$\therefore$ Number of ways of selecting 3 students from 9 students $={ }^9 C_3$
$
\begin{aligned}
& =\frac{9 !}{3 ! \times 6 !} \\
& =\frac{9 \times 8 \times 7 \times 6 !}{3 \times 2 \times 1 \times 6 !} \\
& =84
\end{aligned}
$
$\therefore$ Selection of students is done in 126 ways when 2 specified students are not selected.

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