# Combinatories - Combinatories MCQ

11:

In how many ways can 5 red and 4 white balls be drawn from a hag containing 10 red and 8 white balls ?

 A. 8C5 x 10C4 B. 10C5 x 8C4 C. 18C9 D. None of these Answer Report Discuss Option: B Explanation : Click on Discuss to view users comments. Write your comments here:
12:

Total number of words formed by 2 vowels and 3 consonants taken from 4 vowels and 5 consonants is equal to

 A. 3600 B. 120 C. 7200 D. None of these Answer Report Discuss Option: A Explanation : 3 consonants out of 5 can be selected in 5C3 ways. 2 vowels out of 4 can be selected in 4C2 ways. Therefore, total number of groups each containing 3 consonants and 2 vowels =  5C3  * 4C2 = 5*6=30 Each group contains 5 letters, which can be arranging in 5! ways. Therefore required number of words = 30* 5! = 3600     Click on Discuss to view users comments. Anil Parajuli said: (7:45pm on Tuesday 4th August 2015) 5C3*4C2=10*6=6060*5!=7200 Write your comments here:
13:

How many different committees of 5 can be formed from 6 men and 4 women on which exact 3 men and 2 women serve ?

 A. 6 B. 20 C. 60 D. 120 Answer Report Discuss Option: D Explanation : Click on Discuss to view users comments. Write your comments here:
14:

In how many ways can 5 prizes be distributed among 4 boys when every boy can take one or more prizes ?

 A. 1024 B. 625 C. 120 D. 600 Answer Report Discuss Option: A Explanation : Required number of ways are 45=1024. Since each prize can be distributed in 4 ways Click on Discuss to view users comments. Jeevan Gyawali said: (2:24am on Wednesday 16th August 2017) I don't think the answer is correct in this context. For A to make sense, there needs to be an unlimited supply of the 5 TYPES of prizes. If there are only 5 prizes, the only possible options are :2,1,1,1 -> 4C1 =42,2,1,0 -> 4C2 * 2C1 = 243,1,1,0 -> 4C1 * 3C2 = 123,2,0,0 -> 4C1 * 3C1 = 124,1,0,0 -> 4C1 = 45,0,0,0 -> 4C1 = 4 So, total = 4 24 12 12 12 4 = 68 Write your comments here:
15:

If a five digit number divisible by 3 is to be formed using the numerals 0, 1, 2, 3, 4 and 5, without repetition, then total number of ways this can be done is

 A. 216 B. 240 C. 600 D. 3125 Answer Report Discuss Option: A Explanation : Click on Discuss to view users comments. Write your comments here: