AP EAMCET · Maths · Permutation Combination
Four digit numbers with all digits distinct are formed using the digits \(1,2,3,4,5,6,7\) in all possible ways. If \(p\) is the total number of numbers thus formed and \(q\) is the number of numbers greater than 3400 among them, then \(p: q=\)
- A \(3: 2\)
- B \(4: 3\)
- C \(6: 5\)
- D \(7: 4\)
Answer & Solution
Correct Answer
(A) \(3: 2\)
Step-by-step Solution
Detailed explanation
\(p=\) Total four digit number's formed using \(1,2,3,4\), \(5,6,7={ }^7 C_4 \times 4!=\frac{7!4!}{3!4!}=840\) For number greater than 3400 , Numbers starting with 3,4 are \(={ }^5 C_2 \times 2!=20\) Now, first digit can be \(4,5,6,7={ }^4 C_1 \times{ }^6 C_3 \times 3!=480\)…
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