Ten weight lifters are competing in a team weight-lifting contest. Of the lifters, 3 are from the United States, 4 are from Russia, 2 are from China, and 1 is from Canada. If the scoring takes account of the countries that the lifters represent, but not their individual identities, how many different outcomes are possible from the point of view of scores? How many different outcomes correspond to results in which the United States has 1 competitor in the top three and 2 in the bottom three?

(a) 65536 - the basic principle of counting

(b) 2520 - use the multinomials.  

Step-by-step explanation:

Divide 8 people among 4 schools

The teachers are different among themselves, and so are the schools.  

(a)

Every teacher can choose a school. By the basic principle of counting: 4.4.4.4.4.4.4.4 = 4^8 = 65536

different divisions of the teachers

Note: this does not ensure that every school gets a teacher  

(b) - Every school gets precisely 2 teachers:

to divide 8 different objects into four groups of fixed sizes 2, 2, 2 and 2, use the multinomial coefficient  

( 8   2, 2, 2, 2) = (8!)/(2!2!2!2!) ==> 2520

different divisions of the teachers

points are handed out whenever you post answers.

brainliest answers are handed out by the person asking the question, so whether your answer is picked depends entirely on whether the asker bothers to pick

if you're asking about your rank, it depends on having a certain number of points and a certain number of brainliest answers. for example, at the time of this writing, i have 44338 points out of 15000 needed for the next (nearly triple the requirement! ) but i only have 24 out of 50 required brainliest answers. this number decays, meaning after a certain amount of time (i think about a month), the total number of brainliest answers you've earned doesn't count toward this total. (i've been stuck at the same rank for a long

the lesson to learn here is that you shouldn't worry about points or rank. chances are, no matter how good an answer you may provide, your efforts will go mostly unnoticed unless you focus on the newest/most active questions that get posted.

nswer: a   y-axis

step-by-step explanation: