Question

Let N be the number of ways of choosing a subset of 5 distinct numbers From
{10a +b: 1≤a≤5 , 1≤b≤5}
where a,b are integers, such that no two of the selected numbers have the same units digits and no two have the same tens digit. What is the remainder when N is divided by 737
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Answer 1

Answer:

120 Ways

Step-by-step explanation:

Total possible numbers  are 25

in 5 groups , 5 numbers each

11 , 12 , 13 , 14 , 15

21 , 22 , 23 , 24 , 25

31 , 32 , 33 , 34 , 35

41 , 42 , 43 , 44 , 45

51 , 52 , 53 , 54 , 55

We need to choose 5 distinct numbers

no two of the selected numbers have the same tens digit

=> Each number would be selected from Different Group

Possible Selection from 1 st group woul be 5 as there are 5 numbers

then possible selection from 2nd group would be 4 only as one number will be having same unit digit

Hence total Ways = 5 * 4 * 3 * 2 * 1 = 120

120/737 will give remainder = 120