Question

If Ali selects 3 cards from 5 different cards. In how many different ways can he select the three cards

Answer 1

Ali is picking cards, by nothing is said about an order, so we assume the order doesn't matter.

To calculate the number of ways to select the 3 cards, we can think is steps.

First, we have 5 possibilities to pick from, so we write a 5:

`5`

Then, we have one less option, that is, 4 options, so we multiply by 4:

`5\cdot4`

For the last card, we have one less option, so just 3, thus we multiply by 3:

`5\cdot4\cdot3`

However, this include the various different orders, but we already assumed the order doesn't matter, so we need to divide by the number of way we can permute these 3 cards, which is 3 times 2 times 1. So we can write like that:

`(5\cdot4\cdot3)/(3\cdot2\cdot1)`

Before we calculate all, we can cancel the threes and the 4 with the 2:

`(5\cdot2\cdot1)/(1\cdot1\cdot1)=5\cdot2=10`

Thus, there are 10 ways to select the cards.