# probability and combinatorics

• October 24th 2007, 06:18 PM
jayne
probability and combinatorics
how do i show that the probability of throwing a large straight in yahtzee is 5/162.
• October 24th 2007, 07:22 PM
Soroban
Hello, jayne!

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

Quote:

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: . $P(\text{large straight}) \;=\;\frac{120}{7776} \;=\;\frac{5}{324}$

• October 24th 2007, 07:26 PM
SnipedYou
Soroban don't forget that 1,2,3,4,5 is a large straight as well

So you would have $\frac{2 \cdot 5!}{6^{5}} = \frac{5}{162}$
• October 24th 2007, 07:40 PM
Soroban
I thought 1-2-3-4-5 was called a small straight
. . and 2-3-4-5-6 is the large straight.

• October 24th 2007, 07:42 PM
SnipedYou
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.
• October 24th 2007, 08:03 PM
jayne
thanxs
thanks for all your help to those who helped me out (Handshake)