Q100 / 180 · KCET 2014 · Mathematics

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 ?

Correct answer
A
\( 336 \)
B
\( 337 \)
C
\( 335 \)
D
\( 338 \)

Solution

3 digits from $0,1,2,3,4,5,8,9$ Arrangement of 8 digits taking 3 at a time is 8 $P_{3}=\frac{8 !}{5 !}$ $=8 \times 7 \times 6=42 \times 8=336$

Hence, the correct answer is option: 'A'.

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