The total number of ways of selecting five letters from the letters of the word INDEPENDENT, is

Question

Infinity Learn · Accepted Answer

There are $$11$$ letters in the word $$INDEPENDENT.3N$$, $$3E$$, $$2D$$, I, P, T (6$$ $$types)Different$$ possibilities of choosing $$5$$ letters $$are(A) All different Number of ways $$=6C5$$×$$5$$!$$=6$$×$$120=720$$.(B) $$2$$ alike, $$3$$ differentNumber of ways $$=3C1$$×$$5C3$$×$$5$$!$$2$$!$$=3$$×$$10$$×$$60=1800(C)$$ $$3$$ alike, $$2$$ differentNumber of ways $$=2C1$$×$$5C2$$×$$5$$!$$3$$!$$=$$ $$2$$ × $$10$$ × $$20$$ $$=$$ $$400(D)$$ $$2$$ alike, $$2$$ alike, $$1$$ $$different=3C2$$×$$4C1$$×$$5$$!$$2$$!$$2$$!$$=3$$×$$4$$×$$30=360(E)$$ $$3$$ alike, $$2$$ alike $$=2C1$$×$$2C1$$×$$5$$!$$3$$!$$2$$!$$=$$ $$2$$ × $$2$$ × $$10$$ $$=$$ $$40Hence$$, total number of $$ways=$$ $$720$$ $$+$$ $$1800$$ $$+$$ $$400$$ $$+$$ $$360$$ $$+$$ $$40$$ $$=$$ $$3320$$.

The total number of ways of selecting five letters from the letters of the word INDEPENDENT, is

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