The gift bag from Claire's cosmetics includes 5 bottles of nail polish and 2 tubes of lip gloss.Use p to represent the cost of e
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1) We have that there are (52,3) ways to pick 3 cards out of 52 cards. Also, there are (4,3) ways to pick 3 kings out of the 4 total available kings in the deck. In essence, we need to have one of those ways to be the selected 3 cards. Hence, the probability is the ration (4,3)/(52,3). Computing this:
P=
The probability is very low but not negligible.
2) The Pascal triangle defines a recursive relationship. Hence, we would need to calculate all the binomial coefficients up to 51. Thus, it is not at all practical to use the Pascal Triangle to calculate the ways. It is easier to do the direct computation.
P=
The probability is very low but not negligible.
2) The Pascal triangle defines a recursive relationship. Hence, we would need to calculate all the binomial coefficients up to 51. Thus, it is not at all practical to use the Pascal Triangle to calculate the ways. It is easier to do the direct computation.
There is one critical point at (2, 4), but this point happens to fall on one of the boundaries of the region. We'll get to that point in a moment.
Along the boundary , we have
which attains a maximum value of
Along , we have
which attains a maximum of
Along , we have
which attains a maximum of
So over the given region, the absolute maximum of is 1578 at (2, 44).