In a box, there are 8 alphabets cards with the letters: S,S,A,A,A,H,H,H. Find the probability that the word ASH will form if three cards are drawn simultaneously.
A
928
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B
1928
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C
914
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D
514
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Solution
The correct option is A928 Given, 8 alphabets cards with letters: S,S,A,A,A,H,H,H are present. Three cards are drawn simultaneously, Total no. of outcomes when 3 cards are drawn, N=8C3(2!×3!×3!) (since same letters exist in the set) ⇒N=56 The no. of outcomes to form word ASH, n(X)=2C1×3C1×3C1=18 ∴ The required probability=n(X)N=1856=928