Question

A Supreme Court bench consist of 5 judges in how many ways the bench can give a majority decision

Answer 1

Answer:

Concept: Combinations Problem

For the bench to give a clear majority, 3 judges must support the same statement out of the 5 judges.

Therefore, the formula would be:

nCr = 5C3

$\implies \bf{ nC_{r} = \dfrac{n!}{r!(n - r )!} }\\\\\\\implies \bf{5C_{3} = \dfrac{5!}{3!(5 - 3 )!} }\\\\\\\implies \bf{ 5C_{3} \ \dfrac{ 5 \times 4 \times 3!}{3! \times 2! } }\\\\\\\textbf{3! gets cancelled and we get,} \\\\\\\implies \bf{ 5C_{3} = \dfrac{5 \times 4}{2 \times 1} = \dfrac{20}{2} = 10}$

Hence there are 10 ways in which majority decision can be given

Answer 2

Answer:16

Step-by-step explanation:

Majority comes if either 3,4 Or 5 judges gives same decision.

For 3 judges gives same decision:

5C3 = 5!/2! 3!

= 10;

For 4 judges gives same decision:

5C4 = 5! /4! 1!

= 5;

For 5 judges gives same decision:

5C5 = 1 ( as nCn = 1);

So, total number of ways are:

=5C3+ 5C4+ 5C5

= 10+5+1

= 16.

Hope it will help you all .