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Find out the number of ways in which 5 prizes can be distributed among 5 students such that
(a) Each student may get a prize.
(b) There is no restriction to the number of prizes a student gets. (8)
Ans : (a) Number of ways in which 5 prizes can be distributed between 5 students in such a way that each one may acquire a prize is 5*4*3*2*1 = 5! ways.
(b) While no restriction on the number of prizes a student may get, after that a student may get either 0 or 1 or 2 or...upto 5 prizes. It depicts that a student have six possible ways in which it may get a prize. Hence the number of ways in which prizes can be distributed is 6^{5}.
The adjoining figure shows the cross-section of a railway tunnel. The radius of the tunnel is 3.5m (i.e., OA=3.5m) and ∠AOB=90 o . Calculate : i. the height of the
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