Dark horse

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What seems to be the purpose of the homework?


The answer is 58.

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1 solution

Vivek Bhagat
Mar 24, 2015

Total number of ways to form number is 5 4 3 2 1=120. So now subtracting all the numbers that dont satisfy the given condition. A number starting with 5 would certainly be greater than 43521, and total numbers we can form starting with 5 will be 4 3 2 1=24, similarly number starting with 1 will be smaller than 23415, so that will give another 24 numbers, and numbers with staring 45 and 21 will be larger and smaller than 43521 and 23145 respectively so they each give us 3 2*1=6 numbers,i.e 12 numbers, and then we have the given numbers also,i.e. 23145 and 43521. so total number of ways = 120-24-24-6-6-2=58

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