Question

How many numbers can be formed by using the digits $1,2,3,4,5,6$ without repetition and each number starts with $1$ and ends with $6$?

• A. $24$
• B. $12$
• C. $30$
• D. $25$

Answer 1

Answer: (A)

$24$

Digits are $1,2,3,4,5,6$

1.There would be $1$ two digit number.

2. Three digit number

in between 1 and 6 we can choose any one of the digits in ${}^4{C}_1=4$

3. Four digit number

Choose any $2$ out of $4$ digits.

Therefore , numbers will be ${}^4{C}_2\times 2!=12$

4. Five digit number

Choose any $3$ out of $4$ digits.

Number of ways ${=}^4{C}_3\times 3!=24$

5. Six digit number

Numbers $=4!=24$