How many $7$ digit telephone numbers can be formed from the digits $0, 1, 2, . . ., 9$ , where each telephone number begins with digit $2$ ?

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Solution

We need to form $7$ digit numbers using $0$ to $9.$ The first digit is given is fixed as $2.$ The other $6$ digits can be any of $10$ numbers each.

$\Rightarrow$ Total number of ways

$= 10 \times 10 \times 10 \times 10 \times 10 \times 10$

$= 10^{6}$

Hence, the answer is $10^{6} .$

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How many 7 digit telephone numbers can be formed from the digits 0,1,2,...,9, where each telephone number begins with digit 2?

We need to form 7 digit numbers using 0 to 9. The first digit is given is fixed as 2. The other 6 digits can be any of 10 numbers each.⇒ Total number of ways =10×10×10×10×10×10=106Hence, the answer is 106.

How many $7$ digit telephone numbers can be formed from the digits $0, 1, 2, . . ., 9$ , where each telephone number begins with digit $2$ ?

We need to form $7$ digit numbers using $0$ to $9.$ The first digit is given is fixed as $2.$ The other $6$ digits can be any of $10$ numbers each.

$\Rightarrow$ Total number of ways

$= 10 \times 10 \times 10 \times 10 \times 10 \times 10$

$= 10^{6}$

Hence, the answer is $10^{6} .$