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प्रश्न
Solve the following:
If the letters of the word 'REGULATIONS' be arranged at random, what is the probability that there will be exactly 4 letters between R and E?
उत्तर
The word 'REGULATIONS' has 11 letters, which can be arranged amongst themselves in 11P11 = 11! ways.
∴ n(S) = 11!
Let A ≡ the event that exactly 4 letters are arranged between R and E
If there are exactly 4 letters between R and E, R and E will occupy any of the following 6 positions.
(1, 6), (2, 7), (3, 8), (4, 9), (5, 10), (6, 11)
Now R and E can be arranged amongst themselves in 2P2 = 2! ways.
The remaining 9 letters can be arranged in 9P9 = 9! ways.
∴ n(A) = 6 × 2! × 9!
∴ P(A) = `("n"("A"))/("n"("S"))`
= `(6 xx 2! xx 9!)/(11!)`
= `(2 xx 6 xx 9!)/(11 xx 10 xx 9!)`
= `6/55`
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