Permutations and Combinations
The number of permutation that can made out of the letters of the word "MATHEMATICS". When no two vowels came together is:
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Find the number of ways of selecting 9 balls from 6 red balls, 5 white balls and 5 blue balls if each selection consists of 3 balls of each colour.
Find the number of permutations of the letters of the word ALLAHABAD.
A is a set containing n elements. A subset P1 is chosen and A is reconstructed by replacing the elements of P1. The same process is repeated for subsets P1,P2,….,Pm with m>1. The number of ways of choosing P1,P2,….,Pm so that P1∪P2∪….∪Pm=A is (a)(2m−1)mn (b)(2n−1)m (c)(m+n)Cm (d) none of these
then find the value of n˙
Find the value of n such that (i) nP5=42nP3,n>4 (ii) (n−1)P4nP4=35,n>4
In how many ways can a student choose a programme of 5 courses if 9 courses are available and 2 specific courses are compulsory for every student?
The total number of positive integral solution of 15<x1+x2+x3≤20 is equal to a. 685 b. 785 c. 1125 d. none of these
In how many ways can 2t+1
identical balls be placed in three distinct boxes so that any two boxes together will contain more balls than the third?