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2 answers:
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Using the concept of probability and the arrangements formula, there is a
0.002 = 0.2% probability that the first 8 people in line are teachers.
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- A probability is the <u>number of desired outcomes divided by the number of total outcomes.</u>
- The order in which they are positioned is important, and all people will be positioned, and thus, the arrangements formula is used to find the number of outcomes.
The number of possible arrangements from a set of n elements is given by:
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The desired outcomes are:
- First 8 people are teachers, in <u>8! possible ways.</u>
- Last 4 are students, in <u>4! possible ways.</u>
Thus,
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For the total outcomes, <u>number of arrangements of 12 people</u>, thus:
The probability is:
0.002 = 0.2% probability that the first 8 people in line are teachers.
A similar problem is given at brainly.com/question/24650047
We are given
sequence is 2 , 4 , 8 ,16 , 32 , .....
Firstly , we will check whether it is geometric sequence
Checking geometric sequence:
We will find common ratio between successive terms
and then we check whether they are equal
r1=(second term)/(first term)
r2=(third term)/(second term)
r3=(fourth term)/(third term)
r4=(fifth term)/(fourth term)
we can see that all four ratios are same
so, this is geometric sequence
Calculation of general term:
We got
common ratio is
Let's assume
number of terms is n
first term is 2
now, we can use formula
we can plug values
and we get
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