# 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) - Mathematics

MCQ

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

#### Solution

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

Concept: Permutation and Combination (Entrance Exam)
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