JEE Mains · Maths · STD 11 - 6. permutation and combination
The number of natural numbers less than \(7,000\) which can be formed by using the digits \(0, 1, 3, 7, 9\) (repetition of digits allowed) is equal to
- A \(250\)
- B \(374\)
- C \(372\)
- D \(375\)
Answer & Solution
Correct Answer
(B) \(374\)
Step-by-step Solution
Detailed explanation
\(\boxed{{a_1}}\boxed{{a_2}}\boxed{{a_3}}\) Number of numbers \( = {5^3} - 1\) \(\boxed{{a_4}}\boxed{{a_1}}\boxed{{a_2}}\boxed{{a_3}}\) \(2\) ways for \({a_4}\) Numbers of numbers \( = 2 \times {5^3}\) Required number \(0020 = {5^3} + 2 \times {5^3} - 1\) \(= 374\)
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