Question

How many different (mutually noncongruent) trapeziums can be constructed using four distinct side lengths from the set $\{1,3,4,5,6\}$?

• A. $5$
• B. $11$
• C. $15$
• D. $30$

Answer 1

The correct option is A $5$

Here, the set consist 5 number which is {1,3,4,5,6}.

But to make a trapezium, we have to use only 4 distinct number.

So, choose the 4 number from the set and the total way of choosing 4 number from the set is equal to the number of different (mutually non congruent) trapeziums.

The number of different trapezium $={}^5{C}_4=(5!)/(4!1!)=5$

So, the option (A) is the correct answer.