Question

If 10 teams competing in Single League Tournament, the total number of matches to be played shall be:

a) 30 matches

b) 42 matches

c) 45 matches

d) 48 matches​

Answer 1

All the teams would be playing nine matches , so total number of matches

9 + 8 + 7 + 6 + 5 + 4 + 3 + 2 + 1

Answer ➡ 45 matches

Answer 2

Answer:

Concept:

A permutation is an orderly arrangement of items or numbers. Combinations are a means to choose items or numbers from a collection or set of items without regard for the items' chronological sequence.

Explanation:

"r" things are selected from "n" things in ${ }^{n} C_{r}$  ways.

${ }^{n} C_{r}=\frac{n !}{r ! \times(n-r) !}$

$If r=2 , then { }^{n} C_{r}=n(n-1) / 2$

Given:

10 teams competing in a Single League Tournament

Find:

The total number of matches to be played shall be:

Solution:

To play a match 2 teams are required.

So, to count the number of matches we have to count in how many ways 2 teams are selected from 10 teams.

From the above concept, 2 teams are selected from 10 teams in ${ }^{10} \mathrm{C}_{2}$ ways.

Here,${ }^{10} \mathrm{C}_{2}=10 ! /\{(10-2) ! \times 2 !\}$

                  $\begin{aligned}&\Rightarrow(10 \times 9) / 2 \\&\Rightarrow 5 \times 9 \\&\Rightarrow 45\end{aligned}$

If 10 teams compete in Single League Tournament, the total number of matches to be played shall be 45 matches.

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