Related or not

Probability Level 3

$A=\{1,2,3,\ldots,10\}$ . Find the number of relations in $A\times A$ in which 1 is related to 1 and 10 is not related to 10. If the answer is X, submit $\log_{2}X$

The answer is 98.

1 solution

Prince Loomba
Apr 21, 2016

Total relations: $2^{100}$ . Relations in which 1R1= $2^{99}$ as fixing 1R1 we have to choose any out of 99 and $99 \choose 0$ + $99 \choose 1$ +.......+ $99 \choose 99$ = $2^{99}$ . Similarly remove 10R10. Now we have to choose any out of 98. Thus the answer is $2^{98}$ and $log_{2}(2^{98})=98$

Related or not

The answer is 98.

1 solution

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