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]
Being 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.
Prisha Gupta
8thAbhyas is a complete education Institute. Here extreme care is taken by teacher with the help of regular exam. Extra classes also conducted by the institute, if the student is weak.
Om Umang
10thIt was good as the experience because as we had come here we had been improved in a such envirnment created here.Extra is taught which is beneficial for future.
Eshan Arora
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.
Archit Segal
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.
Shreya Shrivastava
8thI have spent a wonderful time in Abhyas academy. It has made my reasoning more apt, English more stronger and Maths an interesting subject for me. It has given me a habbit of self studying
Yatharthi Sharma
10thIt was a good experience with Abhyas Academy. I even faced problems in starting but slowly and steadily overcomed. Especially reasoning classes helped me a lot.
Cheshta
10thOne of the best institutes to develope a child interest in studies.Provides SST and English knowledge also unlike other institutes. Teachers are co operative and friendly online tests andPPT develope practical knowledge also.
Aman Kumar Shrivastava
10thAbhyas 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
10thMy 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.
