Permutation of Objects Not All Distinct
Permutation Of Objects Not All Distinct
Here we are considering the permutations of a given number of objects when objects are not all different. For example, the number of arrangement of the letter of the word MISSISSIPPI, or the number of six digit number formed by using the digits 1, 1, 2, 3, 3, 4 etc. the permutations can be calculated as.
The number of mutually distinguishable permutations of n things, taken all at a time, of which p are alike of one kind, q alike of second such that p + q = n, is
Case I:
The number of permutations of n things, of which are alike of one kind;
are alike of second kind;
are alike of third;...;
are alike of r th kind such that
is
Case II:
The number of permutations of n things, of which p are alike of one kind, q are alike of second kind and remaining all are distinct, is
Find the number of arrangements of the letters of the word INDEPENDENCE. In how many of these arrangements (i) do the words start with P (ii) do all the vowels always come together | |||
| Right Option : C | |||
| View Explanation | |||
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Aman Kumar Shrivastava
10thAbhyas institute is one of the best coaching institute in the vicinity of Ambala Cantt area. The teachers of the institute are well experienced and very helpful in solving the problems of the students.The good thing of the institute is that it is providing extra classes for the students who are w...
