If a represents the number of permutations of (x$$ $$+$$ $$2) things taken together, b represents the number of permutations of $$11$$ things taken together out of x things, and c represents the number of permutations of (x$$ – $$11) things taken together so that a $$=$$ $$182bc$$, then x $$=$$

Question

If a represents the number of permutations of (x$$ $$+$$ $$2) things taken together, b represents the number of permutations of $$11$$ things taken together out of x things, and c represents the number of permutations of (x$$ – $$11) things taken together so that a $$=$$ $$182bc$$, then x $$=$$

Infinity Learn · Accepted Answer

$$a=x+2Px+2$$,$$b=xP11$$,$$C=x$$−$$11Px$$−$$11$$⇒ $$a=(x+2)$$!,$$b=x$$!(x$$−$$11)!,$$c=(x$$−$$11)$$!Now, a $$=$$ $$182$$ bc⇒(x+2)!$$=182x$$!(x$$−$$11)!(x$$−$$11)!⇒$$(x+2)(x+1)x$$!$$=182x$$!⇒$$(x+2)(x+1)=182=14$$×$$13$$⇒$$x+1=13$$∴$$x=12$$

If a represents the number of permutations of (x + 2) things taken together, b represents the number of permutations of 11 things taken together out of x things, and c represents the number of permutations of (x – 11) things taken together so that a = 182bc, then x =

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