Question

a kindergarten class consists if 11 boys and 14 girls. How many ways can the following be done? Write final answer in number form.

(a) six students are to be selected for the Naptime Committe

(b) In the above Naptime comitte, at least two boys and two girls must be on the committe

(c) a gold start, a green start, a red star, and a blue star are each to ve awarded to one student. Assume no student receives more than one star.

(d) thurty-five (identical) candies are to be distributed amongst the students with each receiving at least one

Answer 1

There are 11 boys and 14 girls that is total of 11+14=25 students.

a) we have to choose 6 students from 25, that we can done in

b) there will be three cases

2 boys 4 girls ( 2 boys can be choosen from 11 in ways and 4 girls from 14 in ways, total will be )

3 boys 3 girls( 3 boys can be choosen from 11 in ways and 3 girls from 14 in ways, total will be )

4 boys 2 girls( 4 boys can be choosen from 11 in ways and 2 girls from 14 in ways, total will be )

All together total number of ways is 55055+60060+30030=160160

c)   Choose one student from 25 and give gold, from the remaining 24 students choose 1 and give green star, remaining 23 students choose 1 and give red star, from the remaining 22 choose 1 and give blue star.

This process can be calculated as

d) We find the solution to this problem using star and bar method .

The number of ways to distribute 35 identical candles to 25 students is