Answer: none of the above
Step-by-step explanation: when performing an hypothesis test and we want to make conclusion by comparing the p-value with the level of significance α
When p is greater than α, we reject the null hypothesis because it simply implies that we have a larger chance to commit a type 1 error ( α is the probability of committing a type 1 error an error where we reject the null hypothesis instead of accepting it ) which means we reject the null hypothesis.
When p is lesser than level of significance α, it means that we have a lesser chance of committing a type 1 error, which means we accept the null hypothesis.
Answer:
60,480 is the correct answer.
Step-by-step explanation:
First of all, let us have a look at the <em>formula of factorial of a number 'n'</em>:

i.e. multiply n with (n-1) then by (n-2) upto 1.
<em>Keep on subtracting 1 from the number and keep on multiplying until we reach to 1.</em>
<em></em>
So,
can be written as: 
Similarly
can be written as: 
Re-writing
:

Now, the expression to be evaluated:

Answer:
50 i think
Step-by-step explanation:
Answer:
They can be seated in 120 differents ways.
Step-by-step explanation:
Taking into account that there are 3 couples and every couple has an specific way to sit, for simplify the exercise, every couple is going to act like 1 option and it's going to occupy 1 Place. If this happens we just need to organize 5 options (3 couples and 2 singles) in 5 Places (3 for a couple and 2 for the singles)
It means that now there are just 5 Places in the row and 5 options to organized. So the number of ways can be calculated using a rule of multiplication as:
<u> 5 </u>*<u> 4 </u>* <u> 3 </u> * <u> 2 </u> * <u> 1 </u> = 120
1st place 2nd Place 3rd place 4th Place 5th Place
Because we have 5 options for the 1st Place, the three couples and the 2 singles. Then, 4 options for the second Place, 3 options for the third place, 2 for the fourth place and 1 option for the 5th place.
Finally, they can be seated in 120 differents ways.
Answer:
.
Step-by-step explanation:
Since repetition isn't allowed, there would be
choices for the first donut,
choices for the second donut, and
choices for the third donut. If the order in which donuts are placed in the bag matters, there would be
unique ways to choose a bag of these donuts.
In practice, donuts in the bag are mixed, and the ordering of donuts doesn't matter. The same way of counting would then count every possible mix of three donuts type
times.
For example, if a bag includes donut of type
,
, and
, the count
would include the following
arrangements:
Thus, when the order of donuts in the bag doesn't matter, it would be necessary to divide the count
by
to find the actual number of donut combinations:
.
Using combinatorics notations, the answer to this question is the same as the number of ways to choose an unordered set of
objects from a set of
distinct objects:
.