![]() ![]() The number of Combinations of ‘n’ different things taking some or all at a time = Number of selection of r consecutive things out of n things along a circle= Number of selection of r consecutive things out of n things in a row = n – r + 1 Number of selections of r things from n things when p particular things are not together in any selection = nC r – n-pC r-p Number of combinations of n distinct objects taking at a time, when k particular objects never occur = Number of combinations of n distinct things taking r at a time, when k particular objects always occur =. ![]() Hence 5 prizes can be given 4 × 4 × 4 × 4 × 4 = 4⁵ ways. Solution: Any one of the prizes can be given in 4 ways then any one of the remaining 4 prizes can be given again in 4 ways, since it may even be obtained by the boy who has already received a prize. The number of permutations of ‘n’ different things, taking ‘r’ at a time, when each thing can be repeated ‘r’ times = nrĮxample 13: In how many ways can 5 prizes be given away to 4 boys, when each boy is eligible for all the prizes? Solution: In the word MISSISSIPPI, there are 4 I’s, 4S’s and 2P’s. Įxample 12: How many different words can be formed with the letters of the world MISSISSIPPI. The number of permutations of ‘n’ things taken all at a time, when ‘p’ are alike of one kind, ‘q’ are alike of second, ‘r’ alike of third, and so on. Number of permutations of n different things taking all at a time, in which m specified things never come together = n!-m!(n-m+1)! ![]() of ways when e & i are together = 5! – 48 = 72
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