NCERT Class XI Mathematics - Permutations and Combinations - Solutions
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Question : 31
Total: 41
How many words, with or without meaning, each of 2 vowels and 3 consonants can be formed from the letters of the word DAUGHTER?
Solution:
Total no. of letters in the word DAUGHTER = 8,
No. of vowels in the word (A, U, E) = 3
No. of consonants in the word (D, G, H, T, R) = 5
So, words can be formed with 2 vowels & 3 consonants in
C 2 ×
C 3
∴ Required no. of words =
P 5 ×
C 2 ×
C 3
=
×
×
No. of vowels in the word (A, U, E) = 3
No. of consonants in the word (D, G, H, T, R) = 5
So, words can be formed with 2 vowels & 3 consonants in
∴ Required no. of words =
=
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