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

Question

How many 5-digit telephone number can be constructed using the digits 0 to 9 , if each number starts with 67 and no digits appears more than once? (A) 335 (B) 336 (C) 338 (D) 337

Tardigrade Admin · Accepted Answer

Since, telephone number start with 67 , so two digits is already fixed. Now, we have to do arrangement of three digits from remaining eight digits.

∴

Possible number of ways

=^{8} P_{3}

= \frac{8 !}{( 8 - 3 )!} = \frac{8 !}{5 !} = 8 \times 7 \times 6 = 336 ways

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

335

336

338

337

Since, telephone number start with 67 , so two digits is already fixed. Now, we have to do arrangement of three digits from remaining eight digits. ∴ Possible number of ways =8P3​ =(8−3)!8!​=5!8!​=8×7×6=336 ways

Since, telephone number start with 67 , so two digits is already fixed. Now, we have to do arrangement of three digits from remaining eight digits.
$∴$ Possible number of ways $=^{8} P_{3}$
$= \frac{8 !}{( 8 - 3 )!} = \frac{8 !}{5 !} = 8 \times 7 \times 6 = 336 ways$