Answer:
i) There are 40320 possible orders
ii) There are 336 possible orders for the first 3 positions.
Step-by-step explanation:
Given: The number of finalists = 8
The number of boys = 3
The number of girls = 5
To find the number of sample point the sample space S for the number of possible orders, we need to find factorial of 8!
The number of possible orders = 8!
= 1 x 2 x 3 x 4 x 5 x 6 x 7 x 8
= 40320
ii) From all 8 finalist, we need to choose first 3 position. Here the order is important. So we use permutation.
nPr =
Here n = 8 and r = 3
Plug in n =8 and r = 3 in the above formula, we get
8P3 =
=
= 6.7.8
= 336
So there are 336 possible orders for the first 3 positions.
Given:
To find:
The highest and lowest scores Sam could have made in the tournament.
Solution:
We have,
It can be written as
Add 288 on both sides.
and
and
Therefore, the highest and lowest scores Sam could have made in the tournament are 290 and 286 respectively.
Answer:
The no. of possible handshakes takes place are 45.
Step-by-step explanation:
Given : There are 10 people in the party .
To Find: Assuming all 10 people at the party each shake hands with every other person (but not themselves, obviously) exactly once, how many handshakes take place?
Solution:
We are given that there are 10 people in the party
No. of people involved in one handshake = 2
To find the no. of possible handshakes between 10 people we will use combination over here
Formula :
n = 10
r= 2
Substitute the values in the formula
No. of possible handshakes are 45
Hence The no. of possible handshakes takes place are 45.
Answer:
Probability that Adam and Ella will be selected:
Step-by-step explanation:
Probabilities
The probability of a random event E to occur is a real number between 0 and 1, both inclusive, where 0 indicates an impossible event and 1 a sure event. There are many techniques to compute probabilities depending on the particular situation and distribution.
This question will be solved by simple calculations and logic, given its simplicity. We know the middle school chess club has 5 members: Adam, Bradley, Carol, Dave, and Ella. Two of them are going to be selected at random to participate in the county chess tournament. We can calculate the number of different ways it can be done without any restriction. It's called the sample space.
The sample space of this event is the combination of 5 members regardless of their position. If {a,b,c,d,e} are the five members, then the possible combinations are {ab,ac,ad,ae,bc,bd,be,cd,ce,de}. Notice that there are only 10 possibilities because the combination ab is the same as ba since it's the same team for the tournament.
We can see there is only one combination of two specific letters out of 10. If a=Adam and e=Ella, only one combination is ae, the other 9 don't include both members, so the probability is