I have no idea how to figure this problem out I know I need

I have no idea how to figure this problem out. I know I need to use the inclusion-exclusion principle and possibly stirling numbers but I\'m not sure. A step by step process would help, thanks!

Solution

total 10 books all differents

We have to make 4 groups with each have atleast one

1) 1,1,1 and 7

total no of ways = 10!/(1!*1!*1!*7!*3!) *4! =2880

2) 1,1, 2, 6

total no of ways = 10!/(1!*1!*2!*6!*2!) *4! =30240

3) 1,1,3,5

total no of ways = 10!/(1!*1!*3!*5!*2!) *4! =60480

4) 1,1,4,4

total no of ways = 10!/(1!*1!*4!*4!*2!*2!) *4! =37800

5) 1,2,3,4

total no of ways = 10!/(1!*2!*3!*4!) *4! =302400

6) 1,2,2,5

total no of ways = 10!/(1!*2!*2!*5!*2!) *4! = 90720

7) 2, 2,2,4

total no of ways = 10!/(2!*2!*2!*4!*3!) *4! = 75600

8) 2,2,3,3

total no of ways = 10!/(2!*2!*3!*3!*2!*2!) *4! = 151200

so final tatal no of ways

= 2880 + 30240 + 60480 + 37800 + 302400 + 90720 + 75600 + 151200 = 751320

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PLEASE RATE SIR!!

I SPENT A LOT OF TIME ON THIS SOLUTION!!

THANKS !!!