Difficult S1 questions..!

Hello here are some stats questions which i need help on, thanks a lot guys in advance!

(1)A class contains 30 children , 18 girls and 12 boys. Four complimentary theatre tickets are distributed at random to the children in the class. What is the probability that:

(a) All four tickets go to girls
(b) Two boys and two girls receive tickets.

(2) How many different 7-digit numbers can be formed from the digits 0,1,2,2,3,3,3. assuming that a number cannot start with 0?

How many of these numbers will end in 0?

From John

Reply 1

Kolya

17

(1)

\huge ({\frac{18}{30}})*({\frac{17}{29}})*({\frac{16}{28}})*({\frac{15}{27}}) = {\frac{68}{609}}

Reply 2

*LEGEND*

1.a. 18/30 X 17/29 X 16/28 X 15/27
b. 18/30 X 12/29 X 17/28 X 11/27 X 4

May be wrong!

Reply 3

*LEGEND*

you need four lots of part b. because there are 4 ways in which 2 girls and 2 boys get tickets

Reply 4

Neo1

OP

4

Isnt there a way to calculate part (a) and (b) using permutations and combinations.... and i dont understand part (b) do you mind explaining it if you can please...

Thanks
From John

Reply 5

*LEGEND*

Yeah, permutations and combinations is a better way

Okay so all 4 to girls means 18C4
But thats not it because to find the probability you must divide by the unrestricted, which is 30C4, which gives the same answer as above. The 'C' is a calculator button meaning combination as im sure you know,

For part b. it will be 18C2 X 12C2 all divided by the unrestricted 30C4

Hope this helps

Reply 6

Neo1

OP

4

*LEGEND*

Yeah, permutations and combinations is a better way

Okay so all 4 to girls means 18C4
But thats not it because to find the probability you must divide by the unrestricted, which is 30C4, which gives the same answer as above. The 'C' is a calculator button meaning combination as im sure you know,

For part b. it will be 18C2 X 12C2 all divided by the unrestricted 30C4

Hope this helps

Yeah thats right, but what about question 2 I find that one quite hard...

Thanks
From John

Reply 7

vickyhunt

10

doing these exact questions now, felt obliged to say thanks :biggrin:

Reply 8

theterminator

1

question 2:

\displaystyle \frac{4!}{2! * 2!} * \frac{18*17*12*11}{30*29*28*27}

Reply 9

davros

16

Original post by vickyhunt

doing these exact questions now, felt obliged to say thanks :biggrin:

You found a thread from 2006 to help you out! This must be some sort of record!!

Reply 10

vickyhunt

10

Original post by davros

You found a thread from 2006 to help you out! This must be some sort of record!!

Yep hahahaha, still on the exercise! If it wasn't for the internet I'd be lost...
Are you any good at stats? - I have one last question to answer which I'm stuck on.

Omg im going to fail so badly