Four books are lined up on a shelf and there are books total to choose from. Nex

Question

Four books are lined up on a shelf and there are books total to choose from. Next to the books we place three dvd's and there are five local to choose from. How many ways can this be done Order matters Order doesn't matter A five digit combinations lock is made from the digits {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}, where repetition is allowed, but with the restriction that the last digit must be even and the first digit cannot be zero. How many lock combinations are there? You play a lotto game where you pick six numbers from the set {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}, where repetitions is allowed, and you win if any permutation of your given numbers is drawn. Suppose you Pick the numbers 0, 0, 5, 5, 5, 5, then what's the probability that you win? Chris Lewis to take his exam and tells friend Stew that there is a probability of 0.31 that he will be late. Stew says that will be late with a probability of 0.12. If the probability that at level is late is 0.39, what is the probability that both are late?

Explanation / Answer

2 ) Numbers are from 0 to 9 , so total 10 numbers are available for combination lock

Lock is of 5 digit combination

last digit must be even and the first digit is not zero

let say that each place/position of the digit is P1 P2 P3 P4 P5

So P1 can be filled in 9 ways , as we cant use 0

no restrictions on places/positions P2 P3 P4 , so each place can be filled in 10 ways

P5 has a restriction that it has to be even , so only numbers 0 2 4 6 8 can be used , so P5 can take 5 values in 5 ways

so total combination is

9*10*10*10*5 = 45000 ways or combinations possible

Please note that we can answer only 1 full question at a time , as per the Chegg answering guidelines

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