Question

Solve the following question and mark the best possible option.
If x, y, z, w, s are natural number If x, y, z, w, s are natural numbers such that 12 < x < y < z < 40 < w < s < 50, how many values are possible for the set (x, y, z, w, s)

Options

• `""^27"C"_3 xx ""^10"C"_2`

• `""^27"C"_3 xx ""^9"C"_2`

• `""^28"C"_3 xx ""^9"C"_2`

• `""^27"P"_3 xx ""^9P_2`

Answer 1

Since 12 < x < y < z < 40 < w < s < 50, there are 27 numbers between 12 & 40.
So, x, y, z can be chosen in `""^27C_3` ways. There are 9 numbers between 40 & 50.
W, s can be chosen in `""^9C_2` ways.

So, Ans. = `""^27C_3 xx ""^9C_2`