1. (9 points) Bob has ten DISTINCT diecast cars. Three of them are American mode

Question

1. (9 points) Bob has ten DISTINCT diecast cars. Three of them are American models five of them are Italian models, and two of them are English models. How many ways can Bob put these cars on a shelf if (a) there are no restrictions? (b) cars from the same country must be put nesxt to each other? (c) cars from the same country are considered identical? 2. (6 points) Alice has twenty identical cookies that she wants to give to four children. In how many ways she can distribute the cookies if (a) there are no restrictions? (b) every child must receive at least two cookies?

Explanation / Answer

1)

N=10 A=3 I=5 E=2

a) when no restriction then 10 car arrange themself in 10! ways =  3628800 ways

b) cars from same country put next to each other

3 american model can arrange in 3!= 6 ways

5 Italin model can arrange in 5!= 120 ways

2 Europian model can arrange iin 2 ways

now there are three model which can arrange in 3! = 6 ways

Total = 6*120*2*6= 8640 ways

c) cars from same country considerd identical

then there are 3 country car can arrange them in 3! ways = 6

2)

a)

with no restriction

20 to distributed in 4 with no restriction

I.e. either we have to select 4 or 5 or 6 or 7 or 8 -----or 20

i.e 20C4 + 20C5+ 20 C6+----- 20C20 =   1047225

b)

thus either we have to select 8 cookies or 9 cookies or 10 cookies or ------ 20 cookies

= 20 C 8+20C9+20C10+-----20C20 = 910596

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