13. Suppose a bag contains the letters to spell
probability.
a) How many four-letter arrangements are
possible using these letters?
I made 4 separate cases (no double letters, i doubles, b doubles, both b and i doubles) and added them to get 3074 ways. Dunno if this is correct
b) What is the probability that Barb
chooses four letters from the bag in the
order that spell her name?
2/3074
d) What four-letter arrangement would be
most likely to be picked? Explain your
reasoning.
One containing at least one i and b.
Can anyone tell me if i did this correctly, the solutions does not have the answer for this question.
Hello, ibetan!
I assume "arrangements" means that the order of the letters is considered.
That is, we are spelling four-letter "words".
There are four cases:13. Suppose a bag contains the letters to spell PROBABILITY.
a) How many four-letter arrangements are possible using these letters?
. . (1) BB and II
. . (2) BB only
. . (3) II only
. . (4) No doubles
(1) BB and II
There are: . arrangements with
(2) BB only
We have: .
Choose two different letters from the other 8 letters: . ways.
Then can be arranged in: . ways.
Hence, there are: . arrangements with only.
(3) II only
We can use the same reasoning from Case (2).
Hence, there are: . arrangements with only.
(4) No doubles
Select and arrange four letters from the nine different letters.
Hence, there are: . arrangements with four different letters.
Therefore, there are: . possible arrangements.
She chooses in that order.b) What is the probability that Barb chooses four letters from the bag
in the order that spell her name?
. .
Therefore: .
A strange question . . . It could have been worded more precisely.d) What four-letter arrangement would be most likely to be picked?
There are 3702 possible four-letter arrangements.
. . And 3024 of them has four different letters.
So, selecting four letters at random,
. . you would get four different letters over 80% of the time.
Which set of four different letters is the most likely?
. . Um . . . all of them?