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The number of all permutations (arrangem...

The number of all permutations (arrangements) of n different objects taken at a time, when a particular object is to be always included in each arrangements is

A

`""^(n-1)C_(r)xx(r-1)!`

B

`""^(n-1)C_(r-1)xxr!`

C

`""^(n-1)C_(r)xxr!`

D

`""^(n)C_(r)xxr!`

Text Solution

Verified by Experts

If a particular object is never taken in each arragement them we first select r objects form the remaining (n-1) objects and then they are arranged.
So, required number of arrangements is `""^(n-1)C_(r)xxr!`
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OBJECTIVE RD SHARMA ENGLISH-PERMUTATIONS AND COMBINATIONS-Chapter Test
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  2. 7 women and 7 men are to sit round a circulartable such that there is ...

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  3. There are (n+1) white and (n+1) black balls, each set numbered 1ton...

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  4. 12 persons are to be arranged to a round table. If two particular pers...

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  5. The number of committees of 5 persons consisting of at least one femal...

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  6. The number of ways in which a team of eleven players can be selected f...

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  7. In a football championship, 153 matches were played. Every two-team pl...

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  8. How many numbers between 5000 and 10,000 can be formed using the digit...

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  9. If x, y and r are positive integers, then ""^(x)C(r)+""^(x)C(r-1)+""^(...

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  10. In how many ways can 5 red and 4 white balls be drawn from a bag conta...

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  11. All the letters of the word 'EAMCET' are arranged in all possible ways...

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  12. There are 10 lamps in a hall. Each one of them can be switched on i...

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  13. How many 10-digit numbers can be formed by using digits 1 and 2

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  14. The straight lines I(1),I(2),I(3) are parallel and lie in the same pla...

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  15. about to only mathematics

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  16. The number of diagonals that can be drawn by joining the vertices of a...

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  17. The sum of the digits in unit place of all the numbers formed with the...

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  18. In an examinations there are three multiple choice questions and each ...

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  19. There are 10 points in a plane, out of these 6 are collinear. If N is ...

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  20. Ramesh has 6 friends. In how many ways can be invite one or more of th...

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  21. If Pm stands for ^m Pm , then prove that: 1+1. P1+2. P2+3. P3++ndotPn=...

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