First slide

Combinations

Question

The number of permutations of letters a, b, c, d, e, f, g so that neither the pattern beg nor cad appears is

Moderate

A

$\frac{7!}{3! 3!}$
B

$\frac{7!}{2! 3! 3!}$
C

4806
D

None of these

Solution

Total number of permutations = 7!
Let A be the property that ‘beg’ occurs.
B be the property that cad occurs.
Number of permutations with A = 5!
= that of with B and $n (A \cap B) = 3!$
$∴ n (A \cup B) = 5! + 5! - 3! = 234$
$∴$ Required number = 7! – 234 = 4806

Get Instant Solutions

When in doubt download our app. Now available Google Play Store- Doubts App

Recieve an sms with download link

Doubts App

OR

SCAN ME

Doubts App

Doubts App