How many words of 4 letters beginning with 'A | vedclass

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(C) The word '$EQUATOR$' consists of $7$ distinct letters: $E, Q, U, A, T, O, R$.We need to form a $4$-letter word starting with '$A$' or '$E$'.Step $

Vedclass · Accepted Answer

$240$

Vedclass · Answer

(C) The word '$EQUATOR$' consists of $7$ distinct letters: $E, Q, U, A, T, O, R$.We need to form a $4$-letter word starting with '$A$' or '$E$'.Step $1$: The first letter must be '$A$' or '$E$'. This can be done in $^2P_1 = 2$ ways.Step $2$: After fixing the first letter,we have $6$ remaining letters available from the word '$EQUATOR$'.Step $3$: We need to fill the remaining $3$ positions using the $6$ available letters. This can be done in $^6P_3$ ways.$^6P_3 = 6 	imes 5 	imes 4 = 120$ ways.Step $4$: The total number of words is the product of the ways to choose the first letter and the ways to fill the remaining positions.Total words $= 2 	imes 120 = 240$.

How many words of $4$ letters beginning with '$A$' or '$E$' can be formed with the letters of the word '$EQUATOR$'?

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