Question

Which of the following are example(s) of combination?

• A. Arrangement of $5$ chocolates taken $3$ at a time.
• B. Permutation of $11$ different things without repetition.
• C. Selection of $6$ officers out of $13$ officers for post of major general of army.
• D. All of the above.

Answer 1

The correct option is C Selection of $6$ officers out of $13$ officers for post of major general of army.

Combination involves selection of "n" different things out of $m$ different things.

Arrangements of things are not done.

Also, order of selection does not matter.

$\underset{–}{Option1}:$Arrangement of $5$ chocolates taken $3$ at a time.

This is a case of arrangements, which is not allowed in combination.

$\underset{–}{Option2}:$ Permutation of $11$ different things without repetition.

Permutations itself means arrangements of things.

So, this is also not example of combination.

$\underset{–}{Option3}:$ Selection of $6$ officers out of $13$ officers for post of major general of army.

This is a selection process which is also known as combination.

So, this is example of combination.