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 | |||
Students / Parents Reviews [10]
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10thA 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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7thMy experience was very good with Abhyas academy. I am studying here from 6th class and I am satisfied by its results in my life. I improved a lot here ahead of school syllabus.
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Shivam Rana
7thAbhyas Methodology is very good. It is based on according to student and each child manages accordingly to its properly. Methodology has improved the abilities of students to shine them in future.
Manish Kumar
10thBeing a parent, I saw my daughter improvement in her studies by seeing a good result in all day to day compititive exam TMO, NSO, IEO etc and as well as studies. I have got a fruitful result from my daughter.
