Question

how many 5 digits telephone number can be constructed using the digits 0 to 9 if each number starts with 67 and number digit appears more than once​

Answer 1

Answer:

the answer is 729.

Step-by-step explanation:

here we use combination.

so total 5 digit no.

_ _ _ _ _

where first two digits are 67

so the remaining three digits are with repeating values are

6 7 _ _ _

= 9×9×9

= 729 ans.

Answer 2

Answer: 336

Explanation;

Total number of digits = 10 i.e., (0, 1, 2, 3,.... , 9)

Now. since each number has to start with 67, thus first two digits of 5 digit number are fixed. We are then left with 8 digits which are to be used to fill up 3 vacant places.

So,Third digit can be selected in 8 ways, fourth digit can be selected in 7 ways and fifth digit can be selected in 6 ways.

So,Total 5 digit numbers that can be constructed = 8 x 7x6 = 336.