Question 143073: These are the questions I'm having problems with:
24.b) (n+2)! / n! = 56
25. solve for n if P(n,3)=2C(n,2),n € N
28. How many 4-digit numbers can be formed from set A= {0,1,2,3,4,5,6} if there is no repetition ( note: 0123 is not a 4-digit number because it equals 123.)
d) How many of the numbers are divisible by 5? (Hint: you must consider 2 cases)
31. A club consists of 25 married couples. Determine ways a committee of 7 people can be formed from these couples a)if there are exactly 5 men on the committee,b) and if there must be at least 3 women and at least 2 men.
33.Find the first five terms in the expansion of (r - 2s)8
First 5 terms in expansion
(r - 2s)8 = (8 under it 0) r8 + (8 under it 1)(r9) (-25) + (8 under it 2)(r6) (-25)2 +(8 under it 3)(r5) (-25)3 + (8 under it 4)(r4) (-25)4
34. The first three terms in the expansion of (1+ay)^n are 1, 12y, and 68y^2
Evaluate a & n. Use the fact that
(1 + ay)n = 1 + nay + n(n-1)/2 (ay)2 + _ _ _
35. Not involving y in expression of ((1/y3(power of 3) +y2)
36. solve for n
b) P(n,5)= 20P(n,3)
Answer by nabla(475)   (Show Source):
You can put this solution on YOUR website! I'm only going to do the first problem here, resubmit the rest and other tutors may assist further.
24.b) (n+2)! / n! = 56
(n+2)!=(n+2)(n+1)n!
Thus, (n+2)(n+1)=56
n^2+3n+2=56
n^2+3n-54=0
(n+9)(n-6)=0
Which implies n=-9 or n=6. We exclude n=-9 because n! has n € N.
n=6.
Check:
8!/6!=8*7=56.
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