when to use combination and permutation in probability please explain

**Permutation and combinations** plays a very important role in probability to find the sample space of an event, number of favourable, total outcomes etc.

For example, in the problem mentioned below we have use the combination to find the required probability of occurrence of any event as:

**From a deck of 52 cards, 2 red cards are removed and the remaining cards are well shuffled. If 8 cards are drawn from these well-shuffled cards, then find the probability that these 8 cards contain at least 2 black cards.**

**Solution:**

When two red cards are removed from a deck of 52 cards, then the remaining numbers of cards = 52 − 2 = 50

8 cards out of these 50 cards can be chosen in ways.

P (At least 2 black cards) = 1 − P (at most 1 black card)

P (At least 2 black cards) = 1 − [P (no black card) + P (1 black card)] … (1)

Out of 8 cards, if no black card is drawn, then 8 red cards should be drawn.

No black card out of 26 black cards can be drawn in way.

8 red cards out of 24 red cards can be drawn in ways.

So, no black card and 8 red cards can be drawn in ways.

∴P (no black card) = P (0 black card and 8 red cards)

Similarly, P (1 black card) = P (1 black card and 7 red cards)

Using equation (1), we obtain

P (At least 2 black cards) = 1 −

**In the same manner permutation is also used in solving the problems based on probability.**

Now, to differentiate between permutation and combination, please go through the below mentioned link.

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