I've been stuck on these problems for a while now...
Using the word "ADJUSTING"
A: How many of these nine-letter arrangements have a consonant in the 5th position and a J in the 6th?
B: How many different 9 letter arrangements can be made?
C: If a nine-letter arrangement is selected at random, what is the probability that a consonant is 5th and J is 6th?
Thanks!
Using the word "ADJUSTING"
A: How many of these nine-letter arrangements have a consonant in the 5th position and a J in the 6th?
B: How many different 9 letter arrangements can be made?
C: If a nine-letter arrangement is selected at random, what is the probability that a consonant is 5th and J is 6th?
Thanks!
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Felisha -
A. There are 5 constants (excluding J) so there are 5 ways to pick 1 constant to fit into position 5. The letter J will fill position 6 and there is only 1 way to do that. That leaves 9 - 2 = 7 letters left to fill in the remaining 7 spaces. There are 7! ways to do that.
In total, we have 5 x 7! = 5 x 5040 = 25,200 arrangements
B. There are 9! = 362,880 different arrangement.
C. Probability = 25,200 / 362,880 = 5/72
Make sense?
Have a GREAT day!
A. There are 5 constants (excluding J) so there are 5 ways to pick 1 constant to fit into position 5. The letter J will fill position 6 and there is only 1 way to do that. That leaves 9 - 2 = 7 letters left to fill in the remaining 7 spaces. There are 7! ways to do that.
In total, we have 5 x 7! = 5 x 5040 = 25,200 arrangements
B. There are 9! = 362,880 different arrangement.
C. Probability = 25,200 / 362,880 = 5/72
Make sense?
Have a GREAT day!