KCET · Maths · Probability
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 & Solution
Correct Answer
(A) \( 336 \)
Step-by-step Solution
Detailed explanation
3 digits from \(0,1,2,3,4,5,8,9\)
Arrangement of 8 digits taking 3 at a time is
8
\(P_{3}=\frac{8 !}{5 !}\)
\(=8 \times 7 \times 6=42 \times 8=336\)
Arrangement of 8 digits taking 3 at a time is
8
\(P_{3}=\frac{8 !}{5 !}\)
\(=8 \times 7 \times 6=42 \times 8=336\)
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