U know li ves the my mans a Iam de him
So since the third place is fixed, we can count that out
organism has8 letters, count out the g since it is fixed
oranism has 7 letters
first slot=7 choices
2nd slot=6 choices (1 choice from 1 slot)
3rd=1 since only g can be here
4rd=5
5th=4
6th=3
7th=2
8th=1
so the answer is 7 times 6 times 1 times 5 times 4 times 3 times 2 times 1 (last one for g)=5040 ways
I'll do problem 13 to get you started.
The expression is the same as
Then we can do a bit of algebra like so to change that n into n-1
This is so we can get the expression in a(r)^(n-1) form
- a = 8/7 is the first term of the geometric sequence
- r = 2/7 is the common ratio
Note that -1 < 2/7 < 1, which satisfies the condition that -1 < r < 1. This means the infinite sum converges to some single finite value (rather than diverge to positive or negative infinity).
We'll plug those a and r values into the infinite geometric sum formula below
S = a/(1-r)
S = (8/7)/(1 - 2/7)
S = (8/7)/(5/7)
S = (8/7)*(7/5)
S = 8/5
S = 1.6
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Answer in fraction form = 8/5
Answer in decimal form = 1.6