First slide

Combinations

Question

Triplet (x, y, z) is chosen from the set {1, 2, 3,, …., n}, such that $x \leq y < z$ .The number of such triplets is

Moderate

A

n³
B

$^{n + 1} C_{3}$
C

$^{n} C_{2}$
D

$^{n} C_{2} +^{n} C_{3}$

Solution

Number of selections when x <y <z $=^{n} C_{3}$
Number of selections when x = y <z $=^{n} C_{2}$
(we have to select only two numbers out of n numbers)
Required number $=^{n} C_{3} +^{n} C_{2} =^{n + 1} C_{3}$

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