Maharashtra State BoardHSC Commerce 11th
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Find the number of arranging 11 distinct objects taken 4 at a time so that a specified object always occurs. - Mathematics and Statistics

Sum

Find the number of arranging 11 distinct objects taken 4 at a time so that a specified object always occurs.

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Solution

There are 11 distinct objects and 4 objects are arranged at a time.
The number of permutations of n distinct objects, taken r at a time, when one specified object will always occur is `"r"xx^(("n"-1))"P"_(("r"-1))"`
Here, r = 4, n = 11
∴ The number of permutations of 4 out of 11 objects when a specified object occurs.
= `4xx^((11-1))"P"_((4-1))=4xx^10"P"_3`

 = `4xx(10!)/((10-3)!)`

 = `4xx(10!)/(7!)`

= `4xx(10xx9xx8xx7!)/(7!)`

 = 2880
∴ There are 2880 permutations of 11 distinct objects, taken 4 at a time, in which one specified object always occurs.

Concept: Concept of Permutations - Permutations When All Objects Are Distinct
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APPEARS IN

Balbharati Mathematics and Statistics 2 (Commerce) 11th Standard HSC Maharashtra State Board
Chapter 6 Permutations and Combinations
Exercise 6.3 | Q 15. (i) | Page 81
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