The number of four-letter words that can be f | vedclass

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Question

(B) To form a four-letter word using the letters $a, b, c$ such that all three letters occur,we must select one letter to be repeated twice and the ot

Vedclass · Accepted Answer

$36$

Vedclass · Answer

(B) To form a four-letter word using the letters $a, b, c$ such that all three letters occur,we must select one letter to be repeated twice and the other two letters to appear once each.Step $1$: Select the letter to be repeated from the set $\{a, b, c\}$. This can be done in $^3C_1 = 3$ ways.Step $2$: Arrange the four letters (e.g.,if $a$ is repeated,the letters are $a, a, b, c$). The number of ways to arrange these four letters is $\frac{4!}{2!} = \frac{24}{2} = 12$.Step $3$: The total number of words is the product of the number of ways to select the letter and the number of ways to arrange them:$3 	imes 12 = 36$.

The number of four-letter words that can be formed with letters $a, b, c$ such that all three letters occur is

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