Question

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

• A. 126
• B. 140
• C. 104
• D. none

Answer 1

Answer: (C)

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