The total number of ways of selecting 4 lette | vedclass

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(D) The word $TSEAMCET$ contains $8$ letters: $T, T, E, E, S, A, M, C$.There are $6$ distinct letters: $\{T, E, S, A, M, C\}$.We need to select $4$ le

Vedclass · Accepted Answer

$36$

Vedclass · Answer

(D) The word $TSEAMCET$ contains $8$ letters: $T, T, E, E, S, A, M, C$.There are $6$ distinct letters: $\{T, E, S, A, M, C\}$.We need to select $4$ letters.Case $1$: All $4$ letters are different.Number of ways $= {}^{6}C_{4} = \frac{6 	imes 5 	imes 4 	imes 3}{4 	imes 3 	imes 2 	imes 1} = 15$.Case $2$: One pair of identical letters and $2$ different letters.Number of ways $= {}^{2}C_{1} 	imes {}^{5}C_{2} = 2 	imes \frac{5 	imes 4}{2 	imes 1} = 20$.Case $3$: Two pairs of identical letters.Number of ways $= {}^{2}C_{2} = 1$.Total number of ways $= 15 + 20 + 1 = 36$.

The total number of ways of selecting $4$ letters from all the letters of the word $TSEAMCET$ is

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