A school has 8 math teachers, 6 English teachers, and 2 geography teachers. From this group, a 5 teacher committee is required. Calculate the number of ways that this committee can be formed if at least one geography teachers must be on the committee.

  1. 👍
  2. 👎
  3. 👁
  1. The number of committees without restrictions is C(16,5) = 4368

    The number of committees without any geography teachers is C(14,5) = 2002

    So the number of ways with at least one geography teacher is 4368-2002 = 2366

    1 geography teacher : C(2,1)*C(14,4) = 2002
    2 geography teachers : C(2,2)*C(14,3) = 364

    sum = 2002+364 = 2366 (as above)

    1. 👍
    2. 👎

Respond to this Question

First Name

Your Response

Similar Questions

  1. statistic

    Assume that the salaries of elementary school teachers in the United States are normally distributed with a mean of $34,000 and a standard deviation of $2000. What is the cutoff salary for teachers in the bottom 10%?

  2. Math

    A group of teachers and pupils attended a concert. The teachers paid $1200 altogether and the pupils paid $640 altogether for their tickets. The price of an adult ticket was $60 and there were 4 more female teachers than male

  3. Math 4

    There are 20 teachers and 705 students in Corey's school. What is the ratio of teachers to students? How would I solve this problem? PLZ help me! :(

  4. Probability

    A committe of 5 members will be chosen from a group of 10 teachers and 5 students. What is the probability that the committee will have A) all teachers? B) 3 teachers and 2 students? C) 3 or 4 teachers?

  1. statistics

    A group of 50 teachers and school administrators attended a convention. If any two persons are picked at random, at least one of the two would be a teacher. From this information, what percentage of the people at the convention

  2. help

    Assume that the salaries of elementary school teachers in the U.S. are normally distributed with a mean of $37,000 and standard deviation of $3500. The cutoff salary for teachers in the bottom 12% is

  3. math

    The student to teacher ratio is 19:1 at a local school and there is a total of 500 students and teachers. How many teachers and how many students are there. I'm not sure how to begin to set this up since I have two unknowns and

  4. math

    Oakland Middle School has 128 6th graders, 121 7th graders , and 135 8th graders. If there are 3 teachers per 32 students, how many total teachers are there?

  1. home, school, and community

    which one of the following statements is NOT true when a partnership is created between a parent and a teacher a. parents are cpable of making major contributions to rheir childs education b.teachers share responsibility and pwer

  2. Math

    A. A survey of 110 teachers showed that 28 of them have a second job. B. A survey of 90 teachers showed that 27 of them have a second job. C. A survey of 70 teachers showed that 21 of them have a second job. D. A survey of 80

  3. Statistics

    An economist found that a random sample of 42 high school teachers had an average annual salary of $56,490. A previous study showed that the population standard deviation is $4150. Find the 99% confidence interval for ยต, the

  4. Math

    Martha recorded the ratio of students and teachers at all the middle schools in the Timber Creek school district. The list is shown below. 20 students : 2 teachers 1 teacher per 15 students 1 teacher per 10 students 40 students :

You can view more similar questions or ask a new question.