First slide

Combinations

Question

Words of length 10 are formed using the letters A, B, C D,E,F,G,H,I,J .Let ‘x’ be the number of such words where no letter is repeated ; and let y be the number of such words where exactly one letter is repeated twice and no other letter is repeated. Then $\frac{y}{9 x}$ =

Moderate

Solution

$x = 10!$
$y =^{10} C_{2} \times 2 \times \frac{10!}{2!} = \frac{\overset{5}{10} \times 9}{2} \times 2 \times \frac{10!}{2!} = 45 \times 10!$
Therefore, $\frac{y}{9 x} = \frac{45 \times 10!}{9 \times 10!} = 5$

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