Get 2 FREE Instant-Explanations on Filo with code FILOAPP

Out of 7 Consonants and 4 vowels, how many words of 3 consonan

Question

Out of 7 Consonants and 4 vowels, how many words of 3 consonants and 2 vowels can be formed?

A

25200

Views: 940 students

Found 8 tutors discussing this question

Mateo Discussed

Out of 7 Consonants and 4 vowels, how many words of 3 consonants and 2 vowels can be formed?

15 mins ago

Discuss this question LIVE

15 mins ago

Text solutionVerified

Number of ways of selecting (

3

consonants out of

7

) and (

2

vowels out of

4

) is given by

^{7} C_{3} \times^{4} C_{2}

= \frac{7 !}{( 7 - 3 )! 3 !} \times \frac{4 !}{( 4 - 2 )! 2 !}

= \frac{7 \times 6 \times 5}{3 \times 2 \times 1} \times \frac{4 \times 3}{2 \times 1}

= 210

Number of groups, each having

3

consonants and

2

vowels

= 210

.

Each group contains

5

letters.

Number of ways of arranging

5

letters among themselves

= 5!

= 5 \times 4 \times 3 \times 2 \times 1

= 120

∴

Required number of ways

= (210 \times 120) = 25200

.

Hence, the answer is

25200

.

Was this solution helpful?

150

Share

Report

One destination for complete JEE/NEET preparation

One destination to cover all your homework and assignment needs

Learn Practice Revision Succeed

Instant 1:1 help, 24x7

Instant 1:1 help, 24x7

60, 000+ Expert tutors

Textbook solutions

Textbook solutions

Big idea maths, McGraw-Hill Education etc

Essay review

Essay review

Get expert feedback on your essay

Schedule classes

Schedule classes

High dosage tutoring from Dedicated 3 experts

Trusted by 4 million+ students

Doubt Icon

Doubt Icon

Stuck on the question or explanation?

Connect with our maths tutors online and get step by step solution of this question.

231 students are taking LIVE classes

Question Text	Out of 7 Consonants and 4 vowels, how many words of 3 consonants and 2 vowels can be formed?
Answer Type	Text solution:1
Upvotes	150