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  4. Four students from University U 1, one of them is Mr. A, and five students from University U 2, one of them is Mr. B, are going to see an Inter University Cricket tournament. However, they found, that only 5 ticket remaining, so 4 of them must go back. Suppose that atleast one student from each University must go to see the game, and at least one of Mr. A and Mr. B must go to see the game. Number of ways of selecting 5 students satisfying the above constraint, is equal to

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Q. Four students from University $U _1$, one of them is $Mr$. A, and five students from University $U _2$, one of them is Mr. B, are going to see an Inter University Cricket tournament. However, they found, that only 5 ticket remaining, so 4 of them must go back. Suppose that atleast one student from each University must go to see the game, and at least one of Mr. A and Mr. B must go to see the game. Number of ways of selecting 5 students satisfying the above constraint, is equal to

Permutations and Combinations

Solution:

$\text { Number of ways }=\text { Total }- \text { (when both } A \text { and } B \text { are excluded }) $
$={ }^9 C _5-{ }^7 C _5=104$