At a family restaurant, the menu has 8 entrees, 12 vegetables, drinks, and 9 des

Question

At a family restaurant, the menu has 8 entrees, 12 vegetables, drinks, and 9 desserts. For a cost of $6.59, you get to choose 1 entree, 3 vegetables, 1 drink, and 2 desserts. How many different plates can be made? S How ALL work FOR CREDIT My ATM card code is made of four single digits (e.g. 3829, this isn't it, so don't even think about 22) it). You can repeat the digits (for example, 8888 is a valid code), the ATM machine is programmed to take the card if three unsuccessful attempts are made. If you try to guess my code what is probability that the machine will take the card (i.e. you fail all three times)? that you are a intelligent thief and do not reuse a code that you have attempted. FOR CREDIT. the work must be correct too.

Explanation / Answer

(21)

1 entree can be selected in 8C1, 3 vegetables can be selected in 12C3 ways

1 drink can be selected in 4C1 ways and 2 deserts can be selected in 9C2 ways

Hence, possible number of plates are 8C1 * 12C3 * 4C1 * 9C2 = 253440

(22)

Number of possible 4 digits codes are 10^4 = 10000

There is only one correct code, hence probability of selecting a correct code p = 1/(10^4) = 0.0001

probability of selecting wrong code 1 - 0.0001 = 0.9999

Probability that all 3 attempts are failed (ATM machine will take the card) = (0.9999)^3 = 0.9997

If the same code is not reentered,

required probability = 9999/10000 * 9998/10000 * 9997/10000 = 0.9994

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