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A bag contains 50 tickets numbered 1, ,2...

A bag contains 50 tickets numbered 1, ,2 3, ...50. Find the number of set of five tickets `x_1< x_2< x_3< x_4< x_5 a n d x_3=30.`

Text Solution

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The correct Answer is:
`.^(29)C_(2)xx .^(20)C_(2)`
Since `x_(1) lt x_(2) lt x_(3) lt x_(4) lt x_(5) " and" x_(3)=30`, therefore, `x_(1),x_(2) lt 30`, i.e., `x_(1) " and" x_(2)` should come from tickets numbered from 1 to 29 and this may happen in `.^(29)C_(2)` ways. Now `x_(4),x_(5)` should come from 20 tickets numbered from 31 to 50 in `.^(20)C_(2)` ways. So, total number of ways is `.^(29)C_(2) .^(20)C_(2)`.
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