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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Hiya Gupta
8thA marvelous experience with Abhyas. I am glad to share that my ward has achieved more than enough at the Ambala ABHYAS centre. Years have passed on and more and more he has gained. May the centre flourish and develop day by day by the grace of God.
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7thAbout Abhyas metholodology the teachers are very nice and hardworking toward students.The Centre Head Mrs Anu Sethi is also a brilliant teacher.Abhyas has taught me how to overcome problems and has always taken my doubts and suppoeted me.
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