If four-letter words (need not be meaningful) | vedclass

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(B) The word $MEDITERRANEAN$ contains $13$ letters: $M(1), E(3), D(1), I(1), T(1), R(2), A(2), N(2)$.We need to form a $4$-letter word of the form $R

Vedclass · Accepted Answer

$59$

Vedclass · Answer

(B) The word $MEDITERRANEAN$ contains $13$ letters: $M(1), E(3), D(1), I(1), T(1), R(2), A(2), N(2)$.We need to form a $4$-letter word of the form $R \_ \_ E$.The two middle positions can be filled in two ways:$1$. Both letters are identical: The available pairs are $(E, E), (A, A), (N, N)$. There are $3$ such pairs.$2$. Both letters are distinct: We choose $2$ distinct letters from the set ${M, E, D, I, T, R, A, N}$. There are $8$ distinct letters available. The number of ways to arrange $2$ distinct letters in the $2$ middle positions is $^8P_2 = 8 	imes 7 = 56$.Total number of words = $3   56 = 59$.

If four-letter words (need not be meaningful) are to be formed using the letters from the word $MEDITERRANEAN$ such that the first letter is $R$ and the fourth letter is $E$,then the total number of such words is

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