The probability of a four-of-a-kind when choosing five cards from a deck, example 58.5

In this video, we solve a problem that seems simple at first glance, but for many students the problem is a challenge. What is the probability you draw a four-of-a-kind when choosing five cards from a deck of 52 cards (for example: 4 kings and the 3 of hearts is a four-of-a-kind hand)?

[Mmichel]

Thank you for the explanation. Spent and embarrassing amount of time looking at this problem with no idea what to do.

[side_walks]

I was searching like four days in row about a good explanation.. and here we are.. thank you so much professor

[emmanuelwhite]

i haven't finished watching this lecture to the end, I already gave it a like. beautiful explanation!

[exlipse]

Very well explained. thinking through the problem is excellent. The explanation of the last choice of 48 possibilities in both ways is great.

[frankied.]

Thank you, I learned a lot. I was recently trying to get into probability math and this really helped me. Thank you!

[FatimaMartinez-drdq]

WOW! the way that you explain it's awesome!!! thanks a lot. Saludos desde Mexico!

[MrNkashani]

Super clear explanation! thank you so much for the video...

[samirezk]

If I have three of a kind... What probability is best.. to get rid of one card or two cards?

[Megaheropap]

How can I calculate the probability of getting 4 kings when choosing 13 cards?

[josemeza]

Does this apply to poker? Because I got 4 cards with the same picture.