Question

How many $5$ digit telephone numbers can be constructed using the digits $0$ to $9$, if each number starts with $67$ and no digit appears more than once ?

• A. 336
• B. 337
• C. 335
• D. 338

Answer 1

Answer: (A)

336

Answer 2

Since, telephone number start with 67 , so two digits is already fixed. Now, we have to arrangement of three digits from remaining eight digits (i.e., $0,1,2,3,4,5,8,9$)
$={ }^{8} P_{3}$ ways $=\frac{8 !}{5 !}$
$=8 \times 7 \times 6$
$=336$ ways