Question: 1. Next week, I'm going to get really fit! On day 1, I'll exercise for 5 minutes. On each subsequent day, I'll exercise 0, 1,

1. Next week, I'm going to get really fit! On day 1, I'll exercise for 5 minutes. On each subsequent day, I'll exercise 0, 1, 2, or 3 minutes more than the previous day. For example, the number of minutes that I exercise on the seven days of next week might be (5, 6, 9, 9, 9, 11, 12). How many such sequences are possible

2.How many positive integers less than or equal to 2023 are divisible by 3, 5 or 7?

3.Prove that the number of different ways 2n students can be paired up is equal to (2n)! /(2power(n)) (n!)

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