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प्रश्न
4 letters are to be posted in 4 post boxes. If any number of letters can be posted in any of the 4 post boxes, what is the probability that each box contains only one letter?
उत्तर
There are 4 letters and 4 post boxes.
Since any number of letters can be posted in all 4 post boxes, so each letter can be posted in 4 different ways.
∴ n(S) = 4 x 4 x 4 x 4
Let event A: Each box contains only one letter.
∴ 1st letter can be posted in 4 different ways.
Since each box contains only one letter,
2nd letter can be posted in 3 different ways.
Similarly, 3rd and 4th letters can be posted in 2 different ways and 1 way respectively.
∴ n(A) = 4 x 3 x 2 x 1
∴ P(A) = `("n"("A"))/("n"("S"))`
= `(4 xx 3 xx 2 xx 1)/(4 xx 4 xx 4 xx 4)`
= `3/32`.
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