## Online Course Discussion Forum

### mc 2a question 2.26

I figured out question 27. I am now stuck on question 30. To be more specific, for question 26, I do not know how to find the number of possibilities for the command group to be formed, but I know the number of possibilities the soldiers can be formed. For question 30, I feel like I am almost there, but I cannot finish it. I already have 8 examples of correct arrangements, but I can't figure out the total amount of them. For example: I already have 123456, 126453, 135462, (ect.) But, I know there is more, because you can sort of rearrange the numbers.

Thanks in advance,

Eddy

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?

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