How to write a proof sequence for an assertion
1 answer:
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Answer:
(a) There are 113,400 ways
(b) There are 138,600 ways
Step-by-step explanation:
The number of ways to from k groups of n1, n2, ... and nk elements from a group of n elements is calculated using the following equation:
Where n is equal to:
n=n1+n2+...+nk
If each team has two students, we can form 5 groups with 2 students each one. Then, k is equal to 5, n is equal to 10 and n1, n2, n3, n4 and n5 are equal to 2. So the number of ways to form teams are:
For part b, we can form 5 groups with 2 students or 2 groups with 2 students and 2 groups with 3 students. We already know that for the first case there are 113,400 ways to form group, so we need to calculate the number of ways for the second case as:
Replacing k by 4, n by 10, n1 and n2 by 2 and n3 and n4 by 3, we get:
So, If each team has either two or three students, The number of ways form teams are:
113,400 + 25,200 = 138,600