Q1 In how many ways a panel of six doctors is selected from five surgeons and six physicians if condition is surgeons are more than physicians.
A 82 B 81 C 65 D 135

Q2 Find the no. of sequences in which seven players can throw a ball,so that the youngest player is not the last.
a 4000 b 2160 c 4320 d 5300

Q3 Ways of choosing two white squares in same row or column on an 8*8 chessboard-

a 12 b 96 c 48 d 60


closed as off-topic by Nikunj, Graham Kemp, M. Vinay, user91500, hardmath May 27 '16 at 13:13

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  • 2
    $\begingroup$ Have you tried anything ? $\endgroup$ – H. Potter May 27 '16 at 12:15
  • $\begingroup$ Welcome to MSE. How far have you got? Q1 What are the possibilities for the number of surgeons? How many ways if you have 5 surgeons and 1 physician? $\endgroup$ – almagest May 27 '16 at 12:16

We have 4 or 5 surgeons among the 6 in the panel. Count these separately. The order does not matter, so we can pick the 4 surgeons in ${5 \choose 4}$ ways followed by ${6 \choose 2}$ ways to pick 2 physicians. Add this to ${5 \choose 5}{6 \choose 1}$ ways to pick all 5 surgeons and 1 physician. The correct answer is not among your answers, BTW, unless you modify a digit..

How many sequences of throws are there in total? Substract all sequences where the youngest throws last, which is essentially all orders with 6 players (as one has a fixed place).

How many rows are there? Then for a fixed row we pick we pick 2 out of 4 (no order) of the white squares in how many ways? Then do the same for columns. (Or the first number times 2).


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