Consider the permutations of the decimal string 000444445555555 that has three 0's, five 4's and seven 5's. For - 0,4,5 let P, be the condition that all x's in the permutation of the string are consecutive, such as in 55555444000 4455 when & -0. Find each of the following without evaluating the factorial numbers, for example, leave 11! as is. Find 1. the total number of permutations of 000444445555555. 2. NP) for -0,4,5 3.S-N(P)-N(Po) + N(P4) + N(P) (0,4,5) 4. S2-MPP) MPP4) + N(PoPs) + N(PAPs) kje (045) kil 5. S3-N(PoP 4Ps) 6. The number of permutations of 000444445555555 in which all 0's or all 4's or all 5's are consecutive. 7. The number of permutations of 000444445555555 which contain none of 000, 44444 and 5555555, such as 445055055440554 8. The number of permutations of 000444445555555 which contain exactly two of 000, 44444, 5555555 as in 444000 455555554 or 55554444455000/5 9. The number of permutations of 000444445555555 which contain at least two of 000, 44444, 555555 as in 444000 455555554, 555544444550005 and 444440005555555