急! F5 排列求Probability 05d2

4a) 7C4
= 35

4b) 56/2^8
= 7/32

5) 10C6/2^10
= 210/1024
= 105/512

6a) 組合有(5,1 / 5,2 / 5,3 / 5,4 / ,5,6)及相反位置各1個
=10

6b) 2x1/6x5/6
= 5/18

4a.
number of combinations for 5 red pieces and 3 green pieces to occur
=number of ways to arrange 5 red pieces and 3 greeen pieces
=8P8/(5!3!)=56

4b.
P(a red piece)=P(a green piece)=1/2
P(5 red and 3 green)=(1/2)⁵(1/2)³×56=7/32

5.
number of ways for 6 red cards and 4 black cards to occur
=10P10/(6!4!)=210
P(6 red and 4 black)
=(1/2)⁶(1/2)⁴×210=105/512

6a
If one of the numbers shown up is '5', then either the 1st throw=5 and 2nd throw≠5,
or 1st throw≠5 and 2nd throw=5
∴there are 2 combinations.

6b
P(one of the numbers shown up is '5')=(1/6)(5/6)×2=5/18