How many license plates would be possible (from problem 4) if the first two char

Question

How many license plates would be possible (from problem 4) if the first two characters must be "AZ"? Timmy has 3 red squares and 2 blue squares that he must put in a line. If the squares of the same color are indistinguishable from each other, then how many ways can he do this? One card is chosen at random from a standard 52 card deck. Find the following probabilities. Answer in fraction form. You need not reduce the fraction. It is a Jack. It is not a Jack. It is a black queen. It is a 4 or a red card. If two cards are selected from a standard 52 card deck, find the following probabilities. Answer in fraction form. You need not reduce the fraction. Both are Aces. No Aces. Exactly one is an Ace Mya is ordering a Ferrari, She must choose between seven colors and then between three different engines. After that, she must choose to get a manual or an automatic. How many different ways can she order the Ferrari.

Explanation / Answer

7) P(its a jack) = 4/52 = 1/13

P(its a black queen) = 2/52 = 1/26

P(its not a jack) = 1-1/13 = 12/13

P(its 4 or red) = (26+2)/52 = 7/13 [26 red cards and 2 black fours, makes a total of 28 red or 4 cards]

8) P(both aces) = 4C2/52C2 = 6/1326 = 1/221

P(no aces) = 48C2/52C2 = 1128/1326 = 188/221

P(exactly 1 ace) = 2x(48/52)x(4/51) = 32/221

9) No of ways possible = 7x3x2 = 42 ways

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