Question

How many $5$ digits telephone numbers can be formed with the digits $0,1,2,.....9$, if each number starts with $35$ and no digits appear more than once?

Answer 1

We have to form $5$ digit telephone number and the first two places are fixed with $35$, thus we have $10-2=8$ digits for $3$ remaining places.

It can be done in ${}^8{P}_3$ ways, i.e.,

Total no. of numbers

$={}^8{P}_3=\frac{8!}{(8-3)!}=8\times 7\times 6=336$

Hence total such telephone numbers are $336$.