1) Mr.Anderson has 3 passenger seats in his car.He offered to drive some of the 5 members of his daughter's club to the movies. How many different groups of 3 passengers could he drive?
2) A jar has green and red marbles.If the ratio of green to red is 3:2,what is the probability that one marble selected at random will be green?
3)The average of the old integers between 10 and 20 is how much more than the average of the even intergers between 0 and 20?
4) In the River City string ensemble of 15 people, 8 people play the violin and 5 people play the cello. If 2 of these people play both instruments,how many members of the string ensemble play neither of these instruments?
3.
[(2 + 4 + 6 + 8 + 10 + 12 + 14 + 16 + 18)/9] - [(11 + 13 + 15 + 17 + 19)/5] = ?
1) 5 choose 3
5C3=5!/(3!2!)=10
2)
3 out of 5 is green, so
P(G)=3/5
3) check if "between 0 and 20" includes or excludes the two ends.
4)
Number of people who play at least one of violin or cello
=8+5-2=11
So four of the members do not play the violin nor the cello.
1) To find the number of different groups of 3 passengers that Mr. Anderson can drive, we can use the combination formula. The formula for combination is given by:
C(n, r) = n! / (r!(n-r)!),
where n is the total number of members (5 in this case) and r is the number of passengers Mr. Anderson needs to drive (3 in this case).
Using the combination formula, we can calculate:
C(5, 3) = 5! / (3!(5-3)!) = (5 * 4 * 3 * 2 * 1) / [(3 * 2 * 1) * (2 * 1)] = 10.
Therefore, Mr. Anderson can drive 10 different groups of 3 passengers.
2) The ratio of green to red marbles is given as 3:2. This means that for every 3 green marbles, there are 2 red marbles.
To calculate the probability of selecting a green marble, we need to consider the total number of marbles. Let's say there are a total of 5x marbles (where x > 0), which gives us 3x green marbles and 2x red marbles.
The probability of selecting a green marble can be calculated as:
P(Green) = Number of green marbles / Total number of marbles = 3x / (3x + 2x) = 3x / 5x = 3/5.
Therefore, the probability of selecting a green marble is 3/5.
3) First, let's find the average of the old integers between 10 and 20. The old integers between 10 and 20 are {11, 12, 13, 14, 15, 16, 17, 18, 19}.
The average of these numbers can be calculated by summing them up and dividing by the total count:
Average of old integers = (11 + 12 + 13 + 14 + 15 + 16 + 17 + 18 + 19) / 9 = 15.
Next, let's find the average of the even integers between 0 and 20. The even integers between 0 and 20 are {0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20}.
The average of these numbers can be calculated by summing them up and dividing by the total count:
Average of even integers = (0 + 2 + 4 + 6 + 8 + 10 + 12 + 14 + 16 + 18 + 20) / 11 = 10.
To find the difference between the averages, we subtract the average of even integers from the average of old integers:
Difference = Average of old integers - Average of even integers = 15 - 10 = 5.
Therefore, the average of the old integers between 10 and 20 is 5 more than the average of the even integers between 0 and 20.
4) To find the number of members in the string ensemble who play neither the violin nor the cello, we can use the principle of inclusion-exclusion.
First, we find the total number of members in the string ensemble, which is 15.
Next, we need to subtract the number of people who play the violin (8) and the number of people who play the cello (5). However, since 2 people play both instruments, we need to add them back in to avoid double-counting.
Therefore, the number of members who play neither instrument can be calculated as:
Total number of members - Number of violin players - Number of cello players + Number of people who play both instruments = 15 - 8 - 5 + 2 = 4.
Therefore, there are 4 members in the string ensemble who play neither the violin nor the cello.
1) To find the number of different groups of 3 passengers Mr. Anderson can drive, we can use the combination formula. The formula for combination is nCr = n! / (r! * (n - r)!)
In this case, Mr. Anderson has 5 members to choose from, and he wants to choose 3 passengers to drive. So we plug in the values into the formula:
n = 5 (the total number of members)
r = 3 (the number of passengers to choose)
nCr = 5! / (3! * (5 - 3)!)
Simplifying,
nCr = 5! / (3! * 2!)
= (5 * 4 * 3!) / (3! * 2)
= (5 * 4) / 2
= 10
Therefore, Mr. Anderson can drive 10 different groups of 3 passengers.
2) To find the probability of selecting a green marble from the jar, we need to know the total number of marbles and the number of green marbles.
Let's say there are 3x green marbles and 2x red marbles (since the ratio of green to red is 3:2).
The total number of marbles in the jar is 3x + 2x = 5x.
The probability of selecting a green marble is the number of green marbles divided by the total number of marbles:
P(green) = 3x / (3x + 2x) = 3x / 5x = 3/5.
So, the probability of selecting a green marble is 3/5.
3) To find the average of a set of numbers, we need to sum all the numbers and then divide the sum by the total count.
First, let's find the sum of the old integers between 10 and 20. The old integers in this range are 11, 13, 15, 17, and 19.
Sum = 11 + 13 + 15 + 17 + 19 = 75.
Next, let's find the average of the even integers between 0 and 20. The even integers in this range are 0, 2, 4, 6, 8, 10, 12, 14, 16, 18, and 20.
Sum = 0 + 2 + 4 + 6 + 8 + 10 + 12 + 14 + 16 + 18 + 20 = 110.
Now, let's find the difference between the two averages:
Difference = Average of old integers - Average of even integers
= 75 / 5 - 110 / 11
= 15 - 10
= 5
Therefore, the average of the old integers between 10 and 20 is 5 more than the average of the even integers between 0 and 20.
4) To find the number of members of the string ensemble who play neither the violin nor the cello, we need to subtract the number of people who play either instrument from the total number of members.
Total members = 15 (given)
People who play the violin = 8
People who play the cello = 5
People who play both instruments = 2
To find the number of members who play neither instrument:
Total members - (People who play the violin + People who play the cello - People who play both instruments)
= 15 - (8 + 5 - 2)
= 15 - 11
= 4
Therefore, there are 4 members of the string ensemble who play neither the violin nor the cello.