# Quantitative Aptitude: Permutations and Combinations Set 3

1. Find out the number of ways in which 6 rings of different types can be worn in 3 fingers?
575
729
615
683
None
Option B
Solution:
The 1st ring can be worn in any of the 3 fingers.
Similarly each of the remaining 5 rings also can be worn in 3 ways.
No of ways=3*3*3*3*3*3=36=729.

2. In a birthday party, every person shakes hand with every other person. If there was a total of 28 handshakes in the party, how many persons were present in the party?
6
12
10
8
None
Option D
Solution:
Let n be the total number of persons present in the party.
No of handshake= [n(n-1)] /2 =28
n(n-1) = 56
n=8.

3. In how many ways 3 boys and 3 girls can be seated in a row so that boys and girls are alternate?
70
68
72
65
None
Option C
Solution:
There are 3boys and 3girls.
Alternate arrangement BGBGBG or GBGBGB
Then ways= (3!*3!) + (3!*3!)
=36+36=72.

4. In how many ways can 4 persons be chosen from 5 boys and 4 girls so as to include exactly one girl?
40
35
50
45
None
Option A
Solution:
Exactly 1 girl 4c1= 4.
Remaining 3person selected from boys 5c3 =10.
Total ways=4*10=40.

5. A student is to answer 5 out of 10 questions in an examination such that he must choose at least 3 from the first five questions. The number of choices available to him is
96
115
87
126
None
Option D
Solution:
Ways 5c3*5c2 + 5c4*5c1 +5c5
=100+25+1
=126ways.

6. In a bag there are five marbles of pink colour and six marbles of blue colour. Two marbles are chosen randomly. What is the probability that both are of same colour?
6/14
5/11
5/14
8/11
None
Option B
Solution:
Probability = 5c2/11c2 + 6c2/11c2
= (5*4)/(11*10) + (6*5)/(11*10)
= 2/11+ 3/11
=5/11.

7. A box contains 5 Green balls, 3 Red balls, 2 Blue balls and 2 Orange balls. If two balls are drawn at random, what is the probability that both are red?
5/11
3/22
1/22
2/11
None
Option C
Solution:
Total balls =5+3+2+2= 12
Probability =3c2/12c2
= (3*2) / (12*11)
= 1/22.

8. From a group of 5 men and 6 women, five persons are to be selected to form a committee so that at least 3 women are there on the committee. In how many ways can it be done?
315
266
325
281
None
Option D
Solution:
Possible ways= 3W and 2M or 4W and 1M or 5W
(6c3*5c2) + (6c4*5c1) + 6c5
[(6*5*4)/(3*2*1) * (5*4)/(2*1)] + [(6*5*4*3)/(4*3*2*1)*5] +6
200+75+6
=281ways.

9. In how many different ways can the letters of the word ‘ APTITUDE ’ be arranged so that the vowels always come together?
1440
1950
2125
1645
None
Option A
Solution:
In a word APTITUDE there are 4vowels A, I, U, E.
Ways= (5! *4! ) / 2!
=1440.

10. A boy has 3 library cards and 8 books of his interest are in the library. Of these 8, he does not want to borrow English part II unless English part I is also borrowed. In how many ways can he choose the three books to be borrowed?
52
41
36
46
None
Option B
Solution:
The first option is he chooses any of the books other then English part 2 = 7c3 = 35
The second option is he selects both the English books and any other book from the remaining options = (2c2 * 6c1) = 6
So total ways=41.