Question

From five persons A, B, C, D, E three persons are selected randomly to form a committee, F
the probability of following events
1) 'C' is not selected in the committee.
2) E' is selected in the committee.
third day. The water was first supplied​

Answer 1

Total no. of ways of selecting three persons randomly from the five persons A, B, C, D and E,

$\sf{\longrightarrow n(S)=\,^5C_3}$

$\sf{\longrightarrow n(S)=10}$

(1)  No. of ways of selection in which C is not included can be obtained by deducting no. of ways in which C must be included, from the total no. of ways.

If C must be included we need to select two persons from the remaining four. So the no. of ways in which C must be included,

$\sf{\longrightarrow n(C)=\,^4C_2}$

$\sf{\longrightarrow n(C)=6}$

Hence the no. of ways in which C is not selected,

$\sf{\longrightarrow n(C')=n(S)-n(C)}$

$\sf{\longrightarrow n(C')=10-6}$

$\sf{\longrightarrow\underline{\underline{n(C')=4}}}$

(2) As in case of C, if E must be included we need to select two persons from the remaining four.

So the no. of ways in which E must be selected,

$\sf{\longrightarrow n(E)=\,^4C_2}$

$\sf{\longrightarrow\underline{\underline{n(E)=6}}}$