Melody

Find the number of ways of arranging the numbers 1, 2, 3, 9 in a circle, so that the sum of any three adjacent numbers is divisible by 3. (Two arrangements are considered the same if one arrangement can be rotated to obtain the other.)

There are none.

sweet   

HAPPY 21ST BIRTHDAY HECTICTAR !

HERE'S  THE  KEY TO YOUR  FUTURE!      

May it be an extremely happy and sucessful one.      

We have 20 people of team A ,20 people of team B and 20 double rooms .How we can put the peaople so that in the rooms we only have people from the same team.

How many ways can 10 rooms be chosen from 20 rooms

20C10 = 184756

Team A can have these or they can have the other set. So that is 2 ways.

Now how many ways can I pair off 20 people?

Person 1 can go with anyone, 19 to chose from

Now there are 18 people left

Person 3 can go with anyone 17 to chose from

so there will be 16 left

and so on.

So that seem to be   19*17*15*13*11*9*7*5*3*1 = = 654729075

I really do not know if that is correct.

So I have

184756*2*654729075*654729075 158398768771746207705000 = 1.5839876877174621 * 10^23

Mmm that is a lot!

That is my best guess. (For the moment)

The digits 1 up to 4 are written on a spinning top. Ella spins the top five times. This way she'll get a number of five digits, like 42313 or 13421

a. How many different numbers can Ella get? 45 = 1024 numbers

4^5=1024 different possibilities     Correct

b. How many different numbers can she get if the number starts with an even digit and then alternates with an odd digit and then an even digit. 25 = 32

even, odd, even, odd, even,    2^5=32       correct

c. How many different numbers can she get if she spins two times a 2, two times a 4 and then one other (1 or 3) digit?

2,2,4,4,  (1 other 2 to chose from)

22441,   or  22443      in any order

5!/(2*2)   each

30 each

60 possibilities    (I'm pretty sure)

1)

The range is the y values, The highest y value (not actually included) is 4.  The curled brackets indicates that neither infinity or 4 are actually included.

hene the  range is   (-infinity, 4)

2)

The arrows are suppose to indicate the direction that the graph will take from that point on.

Hence on the left it goes down for ever and on the right it goes up forever.

Hence the range is   (-infinity, +infinity.)

At a birthday party, 5 boys and 3 girls are seated around a table. 

How many different arrangements are possible if no two girls are seated next to each other?

Normally for these questions rotations are considered to be the same.

Reflections are considered to be different

BUT

Are you interested in gender arangements or individual people arrangements?

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If you are only interested in gender positions then.

Seat a girl first.  She is like the begining of the row.

Now there is 5 boys

GBBBBB

We need to slot in 2 more girls

GB*B*B*B*B

The stars indicate where the other 2 girls can go.

4C2 = 6 gender arrangements are possible.

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If you are interested in the position of individuals then

Stil sit any girl first.  (could have chosen a boy if you wanted to)

Now there is 5 boys and 2 girls left to seat.

Sit the 5 boys first. This can be done in 5! = 120 ways

So we have GBBBBB and we have to sit 2 more girls.

GB*B*B*B*B

4C2*2 = 12 ways.

So that is   120*12 = 1440 individual child arrangements. 

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Rocco is a member of the Aviation Club, which has 12 members.

The members need to choose a 3-person Helicopter Committee and a 4-person Glider Committee.

A member can serve on one of the committees or both. Rocco refuses to serve on both (but he can serve on one of the committees).

In how many ways can they form the committees?

If rocco is on the helicopter committee then

there are   11C2*11C4 = 55*330 = 18150 ways

If rocco is on the Glider committee committee then

there are   11C3*11C3 = 165*165 = 27225 ways

If rocco is not on either committee then

there are   11C3*11C3 = 165*330 = 54450 ways

18150+27225+54450 = 99825 ways

Abraham lincon was our 16th president

our???

He was never president of my country.

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