Question

The number of integers greater then a million that can be formed using the digits $2,3,0,3,4,2,3$ is -

• A. $240$
• B. $320$
• C. $360$
• D. $300$

Answer 1

The correct option is C $360$

How many number greater than a million can be

formed from the number 2,3,0,3,4,2 & 3.

$\to$

1. 2 comes at seventh place from right. The other

six digits can be arranged is 6! ways but these

are three threes, So, $\frac{6!}{3!}$ ways.

2. 3 comes at seventh place from rigid. These

are $\frac{6!}{2!2!}$ ways. $(\because 2$ twos & 2 threes)

3. 4 corners at seventh place from right. These

are $\frac{6!}{3!.2!}$ ways $(\because$ 3 threes & 2 twos)

$\to$ total no. of ways = $\frac{6!}{3!}+\frac{6!}{2!2!}+\frac{6!}{3!.2!}$

$=\frac{6\times 5\times 4\times 3!}{3!}+\frac{6\times 5\times 4\times 3\times 2\times 1}{2\times 1\times 2\times 1}+\frac{6\times 5\times 4\times 3!}{3!\times 2\times 1}$

$=120+180+60$

$=180+180$

$=360$