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  • Give answer! From 6 different novels and 3 different dictionaries, 4 novels and 1 dictionary are to be selected and arranged in a row on ashelf so that the dictionary is always in the middle. The number of such arrangements is :

From 6 different novels and 3 different dictionaries, 4 novels and 1 dictionary are to be selected and arranged in a row on a
shelf so that the dictionary is always in the middle. The number of such arrangements is :

  • Option 1)

    at least 750 but less than 1000

  • Option 2)

    at least 1000

  • Option 3)

    less than 500

  • Option 4)

    at least 500 but less than 750

 

Answers (2)

best_answer

Total cases = _{4}^{6}\textrm{C},_{1}^{3}\textrm{C}, 4 != 1080

i.e at last 1000

 

Theorem of Combination -

Each of the different groups or selection which can be made by taking r things from n things is called a combination.

^{n}c_{r}=\frac{(n)!}{r!(n-r)!}

- wherein

Where 1\leq r\leq n

 

 

The Number of ways of Arrangement of objects -

The number of ways of n different objects taken all at a time =\ ^{n}p_{n}=n!

- wherein

Where 0! = 1

 

 


Option 1)

at least 750 but less than 1000

Option 2)

at least 1000

Option 3)

less than 500

Option 4)

at least 500 but less than 750

Posted by

Himanshu

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