A number x is selected at random from the set {1,2,3,..............99). A number y is selected from the same set.The probability that the number: $7^{X} + 5^{Y}$ last digit is 8.

A number X is selected at random from the number 1 ,2,3,4. Another number Y selected at random from numbers 1,4,9, 16. Find the probability that the product of X and Y is 16.

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A term is selected from the expansion of (x+y+z)10 at random. The probability that two variables out of x, y, z have same power is

The correct option is B 311(x+y+z)10 Total number of terms =12C2=66 Possibilities ⎧⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪⎨⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪⎩5,5,04,4,23,3,42,2,61,1,80,0,10 ∴ Favourable number of cases = 18 ∴ Required probability =1866=311

A term is selected from the expansion of $(x + y + z)^{10}$ at random. The probability that two variables out of x, y, z have same power is