+310 There are 10 numbers, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10. If 1, 2, 3, 4, 5 have to be in that order, 6, 7, 8 have to be in that order, and 9, 10 have to be in that order, how many ways are there to arrange the ten numbers?
You have 10 numbers that are being separated into 3 distinct groups. You have to move the 3 groups, in their ordered way, in 3! =6 ways. It is basically the same as moving 3 digits around, such as 123. You would have 3! =6 ways of arranging them: 123, 132, 213, 231, 312, 321. Place the 5 numbers 1, 2, 3, 4, 5 where 1 is if the 6 arrangements of 123. Then place 6, 7, 8 where 2 is. And finally, place 9, 10 where 3 is. Basically, you will have something like this: [12345678910], [12345910678], [67891012345], [67812345910], [91012345678], [91067812345].
