IIT JEE , AIEEE Forum - Mathematics , Algebra - n digits r taken @ random & multiplied then P(last digit is 1,3,7,9),P(l.. 5),P(2,4,6,8)

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EDIT: the above answer is now correct.

2) For last digit to be 5 at least one digit should be 5 and others should be odd.

Atleast one digit should be 5 means, P(last digit is 5)= ⁿC₁ ( 1/10) ( 5/10) ^n-1= (n/10) ( 5/10) ^n-1

Otherwise , it is like assuming that the first digit is 5.

3)
For last digit to be 2,4,6,8 at least one digit should be among 2,4,6,8 and others can be any digit except 0 and 5.

Again P(last digit is 2,4,6,8) = ⁿC₁ (4/10) ( 8/10)^n-1

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