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

Made by

Davneet Singh

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths and Science at Teachoo.