CPhill

I only differ on 3......

I like Mayland....Notre Dame....and Wisconsin

I'll give this one a shot

The probabilty that 2 planes use runway 1 is (1/2)^2

The probability that 1 plane uses runway 2 is (1/8)^1

The probability of three planes u8se runway 3 is (3/8)^3

And we have 6! arrangements of these probabilities....but some are indistinguishable from others. So, the number of distinguishable arrangements is 6! / [ 2! * 3!] = 60

So the probability is .... 60*(1/2)^2*(1/8)^1*(3/8)*3 = 0.098876953125 = about 9.8%

Since 1 is the square of 1  and 10000 is the square of 100....there must be 100 perfect squares in the first 10000 numbers.

So...the probability of selecting one perfect square is 100/10000 = 1/100 = 1%

y=-x+5 and 5x+2y=14   substituting for y in the seconf equation, we have

5x + 2(-x + 5) = 14       simplify

5x - 2x + 10 = 14

3x + 10 = 14                 subtract 10 from both sides

3x = 4                           divide both sides by 3

x = 4/3

And y = -(4/3) + 5 = 11/3

So...the solution is  (4/3, 11/3)

Wow!!!...nice Tiddle   .....!!!!

I'm not sure about this...but I'll take a stab at it

The probability of red or black = 18/38 = 9/19

And the probability of green = 2/38 = 1/19

So the probability of a ball landing in red 4 times = (9/19)^4

And the probability of a ball landing in black twice is (9/19)^2

And the probability of landing in green once is (1/19)

And note that we have 7! arrangements of  these results......but some are indistiguishable from others

So, the totlal distinguishable arrangements is  7! / [4! 2! ] = 105

So the total probability is given by.... 105*(9/19)^4*(9/19)^2*(1/19) = 0.0624265233650037 = about 6.2%

Yeah...if c is the hypoteneuse....that would be correct....!!

This equals..... [1 - probability of no kings ]

So, the ways to choose no kings is to just select 5 cards from the remaining 48

This is ginen by  C(48,5) = 1712304

And the total way of selecting 5 cards from 52 is C(52,5) = 2598960

So....the probability of at least one king is

1 - 1712304/2598960 = about 34.1%

Solve what???....we're just taking the cosine inverse to find  an angle whose cosine is = to the expression in the parentheses......

Mmmm...I see what Melody is saying.....I think that we would need to account for the other people, as well!!

For each arrangement of the three sitting together, there are 4! ways of arranging the other 4 people.

So, the total arrangements are 30*4! = 720

So

The probability of them not sitting together is

1 - 720/5040 = about 85.7%

I  may think on this one some more !!!