Question No. 32 :
Find the number of ways in which the letters of the word INTERMEDIATE can be arranged taken all at a time so that the vowels are not all together.
[N.B. - Answer with full explanation. No copying. Thank you. ☺]
Answers
Answered by
2
for solution refer attachment
Attachments:
Answered by
1
Solution:
Total no. of vowels=6
Total no. of letters in the word 'INTERMEDIATE'=12
NO.of ways of arranging the consonants of which two are alike=6!
---
2!
=》6×5×4×3×2
_________
2
=》360
NO.of ways of arranging the vowels=
7P6×1 1
--- × ---
2! 2!
=》7! 1 1
--- × --- × ---
1! 3! 2!
=》7×6×5×4×3!
-------------------
3!×2
=》420
Total no.of ways=420×360
=》151200
Total no. of vowels=6
Total no. of letters in the word 'INTERMEDIATE'=12
NO.of ways of arranging the consonants of which two are alike=6!
---
2!
=》6×5×4×3×2
_________
2
=》360
NO.of ways of arranging the vowels=
7P6×1 1
--- × ---
2! 2!
=》7! 1 1
--- × --- × ---
1! 3! 2!
=》7×6×5×4×3!
-------------------
3!×2
=》420
Total no.of ways=420×360
=》151200
Similar questions