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Using all the first five natural numbers,(i) how many numbers can be formed?(ii) how many numbers greater than 30,000 can be formed?(iii) how many numbers divisible by 5 can be formed? |
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Answer» First five natural numbers are 1 2 3 4 5 (i) Total numbers can be formed = 5P5 = 5! = 120 (ii) For the numbers greater than 30,000, the digit at the first place can by any one of the digits 3, 4, 5 and remaining 4 places can be arranged from the remaining 4 digits. .-. Total permutations = 3P1 × 4P4 = 3 × 4! = 3 × 24 = 72 (iii) For the number divisible by 5, the last digit in the humber should be 5. Remaining 4 places can be arranged from the remaining 4 digits accept digit 5. ∴ Total permutations = 1P1 × 4P4 = 1 × 4! = 1 × 24 = 24 |
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