If four whole numbers taken art random are multiplied together, then find the probability that the last digit in the product is 1,3,7, or 9.

Explanation

There are 10 digits 0,1,2…, 9 and any of which can occur in any number at the last place, i.e., at the unit place. It is obvious that if the last digit in any of the four numbers is 0,2,4,5,6,8, then the product of any of such four numbers will not give a number having its last digit as 1,3,7,9, hence, it is necessary that the last digit in each of the number must be any of the four digits 1,3,7,9.
Thus, for each of the four number, the number of ways of selection of the last digit is 10. Favorable number of ways of selection of the last digit is 4.
Therefore the probability that the last digit be any of the four numbers 1,3,7,9 is 4/10 =2/5.
Hence, the required probability that the last digit in each of the four numbers is 1,3,7,9 so that the last digit in their product is `1,3,7,9 is(2//5)^(4)=16//625.`