6 different ways can the two speakers be selected.
On your campus, the members of the Student Activity Council are convening to choose the two speakers for a month-long celebration of artists and performers. The options are Jennifer Lawrence, George Clooney, Leonardo DiCaprio, and Emma Watson.
As we must choose two speakers from a group of six.
[tex]n C r=\frac{n !}{(n-r) ! r !}[/tex]
From the question, n = 4 and r = 2. On substituting
[tex]\begin{aligned}&4 C 2=\frac{4 !}{(4-2) ! 2!} \\&4 C 2=\frac{4 !}{2 ! 2 !} \\&4 C 2=\frac{4 \times 3 \times 2 !}{2 \times 2 !} \\&4C 2=\frac{12}{2} \\&4 C 2=6 \text { ways }\end{aligned}[/tex]
What is combination?
Combination is the process of choosing elements from a collection of elements where the order of the selections is irrelevant. A selection procedure is called a permutation if one of its criteria is the order in which candidates are chosen. The order is irrelevant in combination, a special kind of permutation selection. As a result, there are always more permutations than combinations when choosing 'k' items from 'n' elements.
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