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3. Find the number of permutations of n dissimilar things taken r at a time. |
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Answer» you have 6 numbered balls - from 1 to 6. You need to select 3 balls such that ball that is numbered '4' is always selected. Additionally, you need to arrange them in bags A B and C. In essence you are selecting 2 balls from the remaining 5 balls and subsequently, arranging the 3 balls in bags A B and C.Cases:1.) you can place the ball#4 in A , and arrange the remaining 2 balls in B and C - in 5P2 ways OR2.) you can place the ball#4 in B , and arrange the remaining 2 balls in A and C - in 5P2 ways OR3.) you can place the ball#4 in C , and arrange the remaining 2 balls in B and A - in 5P2 ways so the total cases are 3 x 5P2 i.e. r x (n-1)P(r-1) In short, select 2 balls out of remaining 5 in 5C2 ways and arrange the 3 balls in 3! ways. Hence, 3! x 5C2 = 3 x 5P2 = r x(n-1)P(r-1) |
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