Permutations and Combinations

[mathproblems]

Hello :smile:
Can someone please check my answers
and help me with the last one?
1. How many strings can be formed by ordering
the letters SALESPERSONS if no two S’s are consecutive? 11!/2! ways
2. Refer
to piles of identical red, blue, and green balls where each pile contains at
least 10 balls.
In how many ways can 10 balls be selected if at least one red
ball must be selected? (9+3-1,3-1) =C (11,2)
3. Refer to piles of identical
red, blue, and green balls where each pile contains at least 10 balls.
In how
many ways can 10 balls be selected if at least one red ball, at least two blue
balls, and at least three green balls must be selected? (4+3-1,3-1)
=C(6,2)

4. Find the number of integer solutions of x1 + x2 + x3 = 15
subject to the conditions given.
x1 > or = 1, x2 > or = 1, x3> or =
1
(12+3-1,12)

5. Find the number of integer solutions of x1 + x2 + x3
= 15 subject to the conditions given.
x1 = 1, x2 > or = 0, x3 > or =
0
(14+3-1,14)
6. Find the number of integer solutions of x1 + x2 + x3 = 15
subject to the conditions given.
0 < or = x1 < 6,
1 <or = x2 <
9,
x3 > or= 0
c(15+3-1,15) –[ C6+3-1,6) + C (7+3-1,7)+C(?? ) -
C(??)]