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In how many ways can 5 children the arra...

In how many ways can 5 children the arranged in a row such that two of them, Ram and Shyam, are always together? two of them, Ram and Shyam, are never together?

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Total possible ways=`4[2!]*3! =4*2*6=48`
that should not be taken=`5! =120`
final possible ways=`120-48=72`.
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  16. Compute: (11 !-10 !)/(9!)

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  17. Prove that: 1/(9!)+1/(10 !)+1/(11 !)=(122)/(11 !)

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  18. Find\ x in each of the following: 1/(4!)+1/(5!)=x/(6!)

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  19. Find\ x in each of the following: x/(10 !)=1/(8!)+1/(9!)

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  20. Find\ x in each of the following: 1/(6!)+1/(7!)=x/(8!)

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