In how many ways can 10 instructors be assigned to seven sections of a course in mathematics?
would it be 10/7 = 1.43??
Read the problem carefully.
Think again.
1.43 doesn't make any sense.
oh i did 10/7, but is it 7/10 which is 0.7??
oh wait is it 10*7 = 70 different sections??
Yay! Now you're thinking! They can be assigned in 70 different ways.
yay!!!haha...thanks!!!
No, finding the number of ways to assign 10 instructors to seven sections of a course in mathematics involves a concept called permutations. Permutations are used to find the number of possible arrangements or combinations when order matters.
To solve this problem, we need to use a formula called the multinomial coefficient, which is a generalization of the concept of permutations for multiple groups.
In this case, we have 10 instructors to be assigned to seven sections, which means we need to find the multinomial coefficient for seven groups with sizes 1, 1, 1, 1, 1, 1, and 4 (where four sections will have one instructor each).
The formula to calculate the multinomial coefficient is given by:
C(n; k1, k2, ..., km) = n! / (k1! * k2! * ... * km!)
Using this formula, we can calculate the number of ways as follows:
C(10; 1, 1, 1, 1, 1, 1, 4) = 10! / (1! * 1! * 1! * 1! * 1! * 1! * 4!)
= 10! / (4! * 4!)
= (10 * 9 * 8 * 7) / (4 * 3 * 2 * 1)
= 10 * 3 * 7
= 210
Therefore, there are 210 ways to assign the 10 instructors to the seven sections of the course in mathematics.