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The probability that they each have a different tens digit is 0.047.
What is probability?
The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true. An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty. The likelihood that an event will occur increases with its probability. A straightforward illustration is tossing a fair (impartial) coin. The probability of either "heads" or "tails" is half because there are only two possible outcomes (heads or tails), and because the coin is fair, both outcomes (heads and tails) are equally likely.
Solution:- The collection contains 50 integers, hence there are [tex]^{50}C_5[/tex] different ways to select 5 different integers.
Sample space = [tex]^{50}C_5[/tex]
Each of the five numbers must correspond to one of the five available tens-digits, which are 2 through 6. There are a total of 105 ways to choose the five numbers that satisfy these properties because there are 10 ways to choose a number with a particular set of ten digits (such as 30, 31, or 39).
Therefore,
probability that each have a different tens digit = [tex]\frac{10^5}{^{50}C_5}[/tex]
= [tex]\frac{10\times 10\times 10\times 10\times 10}{^{50}C_5}[/tex]
= [tex]\frac{10\times 10\times 10\times 10\times 10}{\frac{50!}{(50-5)!5!} }[/tex]
= [tex]\frac{10\times 10\times 10\times 10\times 10}{\frac{50!}{45!5!} }[/tex]
= 0.047
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