Home
Class 11
MATHS
Write the total number of words formed b...

Write the total number of words formed by 2 vowels and 3 consonants taken from 4 vowels and 5 consonants.

A

60

B

120

C

7200

D

720

Text Solution

Verified by Experts

The correct Answer is:
C
Given that, total number of vowels = 4
and total number of consonants = 5
Total number of words formed by 2 vowels and 3 consonants
`= ""^(4)C_(2) xx ""^(5)C_(3) = (4"!")/(2"!"2"!") xx (5"!")/(3"!"2"!")`
`= (4 xx 3"!")/(2"!"2"!") xx (5 xx 4 xx 3 xx 2"!")/(3"!" xx 2"!") = (4 xx 5 xx 4 xx 3)/(4)`
`=5 xx 4 xx 3 = 60`
Choose what order they appear in `5"!"` i.e., 120.
So, total number of words `= 60 xx 120 = 7200`
Promotional Banner

Topper's Solved these Questions

  • PERMUTATIONS AND COMBINATIONS

    NCERT EXEMPLAR|Exercise Fillers|9 Videos

  • PERMUTATIONS AND COMBINATIONS

    NCERT EXEMPLAR|Exercise True/False|9 Videos

  • PERMUTATIONS AND COMBINATIONS

    NCERT EXEMPLAR|Exercise Long Answer Type Questions|6 Videos

  • MATHEMATICAL REASONING

    NCERT EXEMPLAR|Exercise OBJECTIVE TYPE QUESTIONS|21 Videos

  • PRINCIPLE OF MATHEMATICAL INDUCTION

    NCERT EXEMPLAR|Exercise OBJECTIVE TYPE QUESTIONS|5 Videos

Similar Questions

Explore conceptually related problems

Total number of words formed by 2 vowels and 3 consonants taken from 4 vowels and 5 consonants is equal to 60 b.120 c.7200 d. none of these

How many different words,each containing 2 vowels and 3 consonants can be formed with 5 vowels and 17 consonants?

What is the number of words formed from the letters of the word 'JOKE',so that the vowels and consonants alternate?

How many words can be formed with 3 vowels and 2 consonants taken from the word 'EQUATION'?

The number of different words that can be formed with 12 consonants and 5 vowels taking 4 consonants and 3 vowels in each word is