2. To see why this is relevant to our analysis of the arrangement of energy in...

2. To see why this is relevant to our analysis of the arrangement of energy in degrees of freedom, first take a simple problem in the ways that you can arrange some cards from a deck.

a. Suppose you have only the numbered cards from one suit (say hearts) of one deck (numbered from Ace = 1 to 10). If you choose 4 of those cards at random, how many different sets of those cards could you get? (Order doesn't matter, so 10-9-8-7 is considered the same as 7-8-9-10.)

b. If you now select from the numbered cards from a different suit (say spades) of that deck and choose 3 of those cards at random, how many different sets of the spades could you get?

c. If you select BOTH four hearts and three spades at random, how many different sets of cards could you get?

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