A) 5 to be chosen among a Total : 10 Men + 8 Women
¹⁸C₅ = (18!)/(5!)(13!) = 8,568 groups of five
b) A must to have men and women. If so we have to deduct all groups of 5 that are all men and all group of 5 that are all women
Groups of 5 with only men: ¹⁰C₅ = 252
Groups of 5 with only women: ⁸C₅ = 56
So number of committees of 5 men and women mixed =
8568 - 252 - 56 = 8,260 committees
c) 3 Women and 2 Men:
⁸C₃ x ¹⁰C₂ = 2,520 groups of 3 W and 2 M
d) More women than men, it means:
3 W + 2 M OR (we have found it in c) = 2,520)
4 W + 1 M OR ⁸C₄ x ¹⁰C₁ →→→→ = 700
5 W + 0 M OR ⁸C₅ x ¹⁰C₀ →→→→ = 56
Total where W>M = 3,276 groups of 5 where women are at least 3
Total miles:350+150=500
Total hours:4+3=7
Avg speed:500/7=71.429 mph
log(x) + log(3) = log(18)
log(x) + 0.477121 = 1.255273
Add -0.477121 to both sides.
log(x) + 0.477121 + −0.477121 = 1.255273 + −0.477121
log(x)+0 = 0.778152
Divide both sides by 1.
log(x)+0/1 = 0.778152/1
log(x)=0.778152
Solve Logarithm
log(x) = 0.778152
10log(x) = 100.778152
x = 100.778152
x = 6.00001
The relative frequency of it landing on tails is 20/30 or 2/3 or 0.667
2t+5v=37 and 4t+3v=39
Solve the first for t
t=18.5-2.5v and use this t in the second equation...
4(18.5-2.5v)+3v=39
74-10v+3v=39
-7v=-35
v=$5.00 and since t=18.5-2.5v
t=$6.00
So tuna sandwiches cost $6.00 and vegetarian sandwiches cost $5.00.
