Probability Help - 11!/(2!*2!) Ways to Arrange

[kring_c14]

1. a.how many ways can you arrange the the letter of the word PROBABILITY?
= my answer for this is 11!/(2!*2!)=9979200

b. how many of these arrangements start with letter B
= itried considering the two B as one, so i have 9!/2!=181440
after this, I am stuck..

c. how may of these arrangements start with a vowel

2. a multiple choice question test consists of 5 questions and 4 possible choice which only one is correct

a. how many ways can a student get no correct answe
b. how many ways can a a student get all correct answers
d. in how many ways can a student get exactly two correct answer

 

[JCVD]

your answer to 1a is correct.
for 1b, to find the number of arrangements of "probability" that start with "b" just put a "b" in front and count the number of ways to arrange the letters of "proability" (your answer puts two "b"s in front and counts the number of ways to arrange the letters of "proaility").
the same idea applies to 1c, except that you have to add up the number of ways to put each different vowel in front.
as for 2, 2b should be obvious for obvious reasons, and you can find the answer to 2a by subtracting your answer to 2b from the total number of ways to fill in the answers to the test.
2d is a bit trickier; just remember that you have to choose from 5 questions exactly 2 to get correct, and then give incorrect answers for the other 3 questions