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Permutations and combinations

 
Swagata Malik
(@swagatamalik)
New Member

In how many ways can seven "mangoes" and five "apples" be arranged in a line so that no two "apples" occur together .

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Topic starter Posted : 29/05/2021 7:26 pm
Nishant Sinha
(@nishant)
Active Member

Ways to arrange 7 mangoes  :  _M_M_M_M_M_M_M_  =   7! 

Now we can place apples in the 8 available places (as shown above in form of blanks). So ways of selecting 5 blank space out 8 is C(8,5) = 8!/(3!*5!)=56

Therefore number of ways of arranging 5 apples = 56*5!

 

Total ways of arranging 7 mangoes and 5 apples = 7!*5!*56

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Posted : 04/06/2021 11:53 pm
Rahul Singh
(@rahul)
Admin

ReplyQuote
Posted : 27/06/2021 3:45 pm
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