So, our friendly number will be 300: it's only two numbers away from 298!
We multiply 300 by 6: it's 1800. (3*6=18, and the 0s we can just add at the end)
now we only need to subtract those two numbers (mupliplied by 6): so we subtract 12.
the result will be 1800-12=1788.
Answer:
I'm not really sure but I think its 6:36
Step-by-step explanation:
12 quarters + 18 nickels + 6 dimes = 36 coins in total
6 dimes in total
6:36
Answer:
![P(FH) = \frac{\binom{13}{1}*\binom{4}{3}*\binom{12}{1}*\binom{4}{2}}{\binom{52}{5}}](https://tex.z-dn.net/?f=P%28FH%29%20%3D%20%5Cfrac%7B%5Cbinom%7B13%7D%7B1%7D%2A%5Cbinom%7B4%7D%7B3%7D%2A%5Cbinom%7B12%7D%7B1%7D%2A%5Cbinom%7B4%7D%7B2%7D%7D%7B%5Cbinom%7B52%7D%7B5%7D%7D)
P(FH) =0.00144
Step-by-step explanation:
The total number of possible poker hands (n) is the combination of 5 out of 52 cards:
![n=\binom{52}{5}](https://tex.z-dn.net/?f=n%3D%5Cbinom%7B52%7D%7B5%7D)
In order to get a full house, first pick one out of 13 cards (13 choose 1), then pick 3 out of the 4 cards of the chosen type to form three of a kind (4 choose 3), now pick another card from the remaining 12 different numbers or faces (12 choose 1), then pick 2 out of the 4 suits to form a pair (4 choose 2)
The probability of getting a fullhouse, in binomial coefficients is:
![P(FH) = \frac{\binom{13}{1}*\binom{4}{3}*\binom{12}{1}*\binom{4}{2}}{\binom{52}{5}}](https://tex.z-dn.net/?f=P%28FH%29%20%3D%20%5Cfrac%7B%5Cbinom%7B13%7D%7B1%7D%2A%5Cbinom%7B4%7D%7B3%7D%2A%5Cbinom%7B12%7D%7B1%7D%2A%5Cbinom%7B4%7D%7B2%7D%7D%7B%5Cbinom%7B52%7D%7B5%7D%7D)
Expanding the coefficients and solving:
![P(FH) = \frac{13*4*12*\frac{4*3}{2*1} }{\frac{52*51*50*49*48}{5*4*3*2}}\\P(FH) =0.00144](https://tex.z-dn.net/?f=P%28FH%29%20%3D%20%5Cfrac%7B13%2A4%2A12%2A%5Cfrac%7B4%2A3%7D%7B2%2A1%7D%20%7D%7B%5Cfrac%7B52%2A51%2A50%2A49%2A48%7D%7B5%2A4%2A3%2A2%7D%7D%5C%5CP%28FH%29%20%3D0.00144)