Answer:
7/n
Step-by-step explanation:
quotient means division and the only answer choice with a division sign is 7/n where n is the unknown number.
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There are NO SOLUTIONS.
Substitute the first equation for y in the second equation. You can see it does not work. 6 does not equal 8. Therefore there are no solutions.
In a hand of 5 cards, you want 4 of them to be of the same rank, and the fifth can be any of the remaining 48 cards. So if the rank of the 4-of-a-kind is fixed, there are
possible hands. To account for any choice of rank, we choose 1 of the 13 possible ranks and multiply this count by
. So there are 624 possible hands containing a 4-of-a-kind. Hence A occurs with probability

There are 4 aces in the deck. If exactly 1 occurs in the hand, the remaining 4 cards can be any of the remaining 48 non-ace cards, contributing
possible hands. Exactly 2 aces are drawn in
hands. And so on. This gives a total of

possible hands containing at least 1 ace, and hence B occurs with probability

The product of these probability is approximately 0.000082.
A and B are independent if the probability of both events occurring simultaneously is the same as the above probability, i.e.
. This happens if
- the hand has 4 aces and 1 non-ace, or
- the hand has a non-ace 4-of-a-kind and 1 ace
The above "sub-events" are mutually exclusive and share no overlap. There are 48 possible non-aces to choose from, so the first sub-event consists of 48 possible hands. There are 12 non-ace 4-of-a-kinds and 4 choices of ace for the fifth card, so the second sub-event has a total of 12*4 = 48 possible hands. So
consists of 96 possible hands, which occurs with probability

and so the events A and B are NOT independent.