91Ó°ÊÓ

A box has 24 bulbs out of which 4 bulbs are defective.

The bulbs are selected without replacement.

The total number of bulbs in a box is 24.

Number of defective bulbs is 4.

Thus, total working bulbs are\(\left( {24 - 4} \right) = 20\)

Formula for selecting r items from total N items is\(^N{C_r} = \frac{{N!}}{{r!\left( {N - r} \right)!}}\)

Number of ways of selecting any 4 defective bulbs from 24 bulbs is\(^{24}{C_4} = \frac{{24!}}{{4!\left( {24 - 4} \right)!}}\).

Number of ways of selecting 4 defective bulb is \(^4{C_4} = \frac{{4!}}{{4!\left( {4 - 4} \right)!}}\).

Probability of selecting all 4 defective bulbs is expressed as,

\(\begin{aligned}{c}\frac{{^4{C_4}}}{{^{24}{C_4}}} &= \frac{{\frac{{4!}}{{4!\left( {4 - 4} \right)!}}}}{{\frac{{24!}}{{4!\left( {24 - 4} \right)!}}}}\\ &= \frac{1}{{10626}}\end{aligned}\)

Therefore, the probability of selecting all 4 defective bulbs is\(\frac{1}{{10626}}\).