# Math Help - probability and combinatorics

1. ## probability and combinatorics

how do i show that the probability of throwing a large straight in yahtzee is 5/162.

2. Hello, jayne!

I assume we are allowed one throw to get the large straight.
. . Then I get a different answer . . .

Show that the probability of throwing a large straight in Yahtzee is 5/162.
The probability of throwing 2-3-4-5-6 (in that order) is: . $\left(\frac{1}{6}\right)^5$

Since there are $5! = 120$ possible orders,
. . then: . $P(\text{large straight}) \;=\;\frac{120}{7776} \;=\;\frac{5}{324}$

3. Soroban don't forget that 1,2,3,4,5 is a large straight as well

So you would have $\frac{2 \cdot 5!}{6^{5}} = \frac{5}{162}$

4. I thought 1-2-3-4-5 was called a small straight
. . and 2-3-4-5-6 is the large straight.

5. No a small straight is 4-in-a-row and a large straight is 5-in-a-row. Well by the rules I play by.

6. ## thanxs

thanks for all your help to those who helped me out