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mc 2a question 2.26

Re: mc 2a question 2.26

On 26, to choose a team you need to make sure that for each soldier, the soldier's boss (sergeant), or the boss of their boss (officer) is also part of the team. First you need to decide if the team will have (i) $2$ officers OR (ii) $6$ sergeants, and then pick the soldiers. For each of the two cases, how many soldiers do you have available? In how many ways can you choose the officers or sergeants?

For 30 try to look at the remainders of the numbers. For example, in 123456 the remainders are 120120, and in 126453 the remainders are 120120. Do you notice a pattern?