Each person in a group of 12 has one pet. Three people have a cat, 2 people have a dog, and the rest have a bird. What is the pr
2 answers:
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We can find a formula for nth term of the given sequence as follows:
1, 5, 12, 22, 35
The 1st differences between terms:
4, 7, 10, 13
The 2nd differences :
3, 3, 3
Since it takes two rounds of differences to arrive at a constant difference between terms, the nth term will be a 2nd degree polynomial of the form: , where c is a constant. The coefficients a, b, and the constant c can be found.
We can form the following 3 equations with 3 unknowns a, b, c:
Solving for a, b, c, we get:
a = 3/2, b = -1/2, c = 0
Therefore, the nth term of the given sequence is:
Answer:
There are 17,418,240 different ways to choose the teams.
Step-by-step explanation:
Arrangements of n elements:
The number of possible arrangements of n elements is given by:
In how many different ways can the teams be chosen so that the number of employees on each project are as follows: 9, 4, 2?
This is:
Arrangement of 9 elements, followed by an arrangement of 4 elements followed by an arrangement of 2 elements. So
There are 17,418,240 different ways to choose the teams.