A combine lock has three numbers in the combination, every in the range 1 – 50. I. How many of the combinations have actually the very first and 2nd number matching? ii. How numerous of the combinations have exactly two of the 3 numbers matching?

For the very first one we have actually 50 options for there first number. Since the an initial number is picked we only have 1 selection for the 2nd since it needs to be the exact same as the first. Since the third number have the right to be something we as soon as again have actually 50 choices. This gives us 50∗1∗50=2500 combinations.

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For the second we have three different scenarios one of two people the an initial two match and also the 3rd is different, the 2nd two match and also the very first is different, or the first and third match and also the 2nd is different. In the first case we as soon as again have actually 50 choices for the very first number and 1 because that the second, yet we only have actually 49 choices for the third number because it have the right to not it is in the same as the first two. Giving us 50∗1∗49=2450 combine in option one. Since the other two alternatives are an extremely similar,each choice will offer you 2450 combinations and you have actually three options. All we need to do is include 2450+2450+2450=7350 combinations.
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