(A) In the word $DAUGHTER$,there are $3$ vowels $(A, U, E)$ and $5$ consonants $(D, G, H, T, R)$.Number of ways to select $2$ vowels from $3$ is $\bin

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(A) In the word $DAUGHTER$,there are $3$ vowels $(A, U, E)$ and $5$ consonants $(D, G, H, T, R)$.Number of ways to select $2$ vowels from $3$ is $\binom{3}{2} = 3$.Number of ways to select $3$ consonants from $5$ is $\binom{5}{3} = 10$.Total combinations of $2$ vowels and $3$ consonants $= 3 \times 10 = 30$.Each combination of $5$ letters can be arranged in $5!$ ways.Total number of words $= 30 \times 5! = 30 \times 120 = 3600$.

Class 11 Mathematics Permutation and Combination Definition of permutation, Number of permutations with or without repetition, Conditional permutations

Medium

How many words,with or without meaning,each of $2$ vowels and $3$ consonants can be formed from the letters of the word $DAUGHTER$?

A
$3600$
B
$7200$
C
$1800$
D
$5400$

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Definition of permutation, Number of permutations with or without repetition, Conditional permutations

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How many words,with or without meaning,each of $2$ vowels and $3$ consonants can be formed from the letters of the word $DAUGHTER$?

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