Please provide working out and explanation. Thanks

Question 4* (Combinations, including 'stars and bars' ) A SplN lS a6d1git PIN (With decimal (llgltS) d1d2d3d4d5d3 StleYlg d+1di = 00131, i=1, . . , 5. 8.9. 344566. How many SPINs are there? (a) First consider SPINs that, like the example, involve all and only the digits 3,4,5,6. We need to choose 6 digits from this set of of 4 possible values, and each value must be chosen at least once. So really we need to choose just two digits from those 4 values, with repeat allowed. How many ways are there to do this? [Two stars, four categories and hence three bars] (b) How many SPINs use exactly four differnt values? (c) Following a similar path to (a) and (b), how many SPINs, like 666788, use exactly three different values? ((1) By considering all the other possibnilitias for the number of values used by a SPIN, calculate the total number of SPINS. (e) [Optional] Can you think of completely different way of attacking this problem, one that doesn't use combinations at all, and use it to check your answer above