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 ?

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

Tardigrade Admin · Accepted Answer

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

Q. 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 ?

336

337

335

338

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) =8P3​ ways =5!8!​ =8×7×6 =336 ways

Q. 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 ?

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