NCERT Class XI Mathematics - Permutations and Combinations - Solutions
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Question : 32
Total: 41
How many words, with or without meaning, can be formed using all the letters of the word EQUATION at a time so that the vowels and consonants occur together?
Solution:
Total no. of letters in the word EQUATION = 8
No. of vowels in the word (E, U, A, I, O) = 5
No. of consonants in the word (Q, T, N) = 3
When vowels & consonants occur together we make two groups, one is of vowels & second is of consonants.
Arrangement of 2 groups =
P 2
Arrangement of vowels in its group =
P 5
Arrangement of consonants in its group =
P 3
So, the required no. of words = 2! × 5! × 3! = 1440.
No. of vowels in the word (E, U, A, I, O) = 5
No. of consonants in the word (Q, T, N) = 3
When vowels & consonants occur together we make two groups, one is of vowels & second is of consonants.
Arrangement of 2 groups =
Arrangement of vowels in its group =
Arrangement of consonants in its group =
So, the required no. of words = 2! × 5! × 3! = 1440.
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