Misc 2
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?
Misc 2
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?
Number of vowels in EQUATION
= E, U, A, I, O
= 5
Number of ways vowels can be arranged = 5P5
= 5!/(5 − 5)!
= 5!/0! = 5!/1 = 120
Number of consonants in EQUATION
= Q, T, N
= 3
Number of ways consonants can be arranged = 3P3
= 3!/(3 − 3)!
= 3!/0! = 3!/1 = 6
Total number of ways in which vowels & consonants occur together
= 2 × (Number of ways vowel arrange)
× (Number of ways consonants arrange)
= 2 × (120 × 6)
= 1440

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.

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