First slide

Combinations

Question

If the difference of the number of arrangements of three things from a certain number of dissimilar things and the number of selections of the same number of things from them exceeds 100, then the least number of dissimilar things is

Moderate

A

8
B

6
C

5
D

7

Solution

${Here,}^{n} P_{3} -^{n} C_{3} > 100$
$\begin{array}{l} or \frac{n!}{(n - 3)!} - \frac{n!}{3! (n - 3)!} > 100 \\ or \frac{5}{6} n (n - 1) (n - 2) > 100 \\ or n (n - 1) (n - 2) > 120 \\ or n (n - 1) (n - 2) > 6 \times 5 \times 4 \\ or n = 7, 8, \dots \end{array}$

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