Question

5. A bag consists of 5 red marble and 6 white marble. Find the number of choosing 4 marble:

a) Without condition

b) With 2 red marble and 2 white marble

c) With the same colours.

6. How many choices are there if we want to make a 5 person committee from 12 persons, if the president has already been chosen?

7. A student was given 15 questions in a test. Find the number of choices if:

a) He must answer 10 questions only.

b) He must answer 10 questions but the first 5 are compulsory.

c) He must answer 10 questions, where the first 5 from Section A question 1 to 8, and another 5 from Section b, question 9 to 15.

d) He must answer 10 questions, where at least 6 question from Section A question 1 to 8.

Answer 1

(there are more than 1 questions, as per policy i am answering first question)

5.

a.

number of choosing 4 marbles =

= (ways to choose all 4 same color) + (ways to choose 3 red, 1 white) + (ways to choose 2 red, 2 white) + (ways to choose 1 red, 3 white)

= 2 (all red and all blue) + 4! / (3!*1!) + 4! / (2!*2!) + 4! / (1!*3!)

= 16

b.

number of ways With 2 red marble and 2 white marble

= 4! / (2!*2!)

= 6

c.

no. of ways With the same colours.

= 2 (all red and all blue)

= 2