break these questions down and explain why the answers are these

1. How many four-digit rumbers can be formed from the following cight digits: 1,2,3,4,5,6,7,8 ? TIE DIGITS ARE NOT REPEATED. 8765P(8,4)=1680 2. In how many ways ean 8 identical History books and 2 different Math books be arranged on a shelf sucb that the Math books are not next to each other? Solution 1: Total - num. ways for Math together 109-9 positions for the pair a 2 ways cach 10929=72 Solution 2: Set aside one History book and then place Math books P(9,2)=98=72 3. Find the number of integer solutions to: X1+X2+X1+X4=14 stabject to: X10,X21,X32, and X13, Set aside X2,X3,X3,X4,X1,X4 11111111 c(11,3)=165 4. The 9 men and 12 women in the Math club need to form a fund raising conamittec. How many comaitles of size 4 can be formed that have more women then men? 4womenandnomen+3womenand1manC(12,4)+C(12,3)C(9,1)+2475OR-C(21,4)C(9,4)C(9,3)=C(12,1)C(9,2)C(12,2)total-allmen-threemen-onewomen-twomen-twowonen