# Quantitative Aptitude: Probability Questions – Set 11

1. In how many ways can 3 roses and 4 tulips 2 jasmines can be arranged in a garland such that all roses tied together and all tulips are tied together and jasmines also tied together?
876
864
867
912
834
Option B
Required number of ways = 3( 3! * 4! *2!)
=3* 3 * 2 * 4* 3 * 2 *2
=>864 ways.

2. In how many ways the word “ note book “ can be arranged?
5670
2456
6720
5670
6120
Option C
notebook.
There are 8 letters. o is repeated three times
So number of words formed=8!/ 3!
=6720 ways

3. There are two positive integers x and y .What is the probability that x+y is even?
1/2
1/3
1/4
1/5
1/6
Option A
Sum of positive integers is either odd or even.
Hence the required probability= ½

4. The sum of three consecutive odd number is 93.Then what will be the middle number if they arranged in descending order?
30
31
29
33
35
Option B
Let the three numbers be 2a +1 , 2a+3, 2a +5
Given 2a+1 + 2a+3 +2a+ 5= 93
=>6a +6 = 93
=> 6a= 84
=>a=14
Hence the numbers are = 29,31,33
So the middle number is 31.

5. A bag contains 6 nestle bars and 4 kitkat bars. Two bars given at random to the children.
Then what is the probability that they are of same bars?
2/15
3/15
5/15
6/25
7/15
Option E
Required probability = 6C2 + 4C2 / 10C2
= 30+ 12/ 90 = 42/90
=7/15

6. In how many different words can be formed from word ENCYCLOPEDIA such that all vowels come together?
20150
20140
20160
20980
20790
Option C
NCYCLPD(all vowels)
So number of letters= 8 also c is repeated twice.
Required probability = 8!/ 2! = 20160 ways

7. Out of all the 2-digit integers between 1 and 50, a 2-digit number has to be selected at random.
What is the probability that the selected number is not divisible by 13?
31/40
32/40
25/40
33/40
37/40
Option E
There are total 40 two digit numbers, out of them 3 are divisible by 13, these are 13, 26, 39
Therefore, probability that selected number is not divisible by 13 = 1 – 3/40 = 37/40

8. How many different words can be arranged with letters of the word STENCIL when vowels occupied even places?
620
720
360
440
580
Option B
Vowels are 2, places are 3. So they are arranged in 6 ( 3C2 * 2! ) ways.
Consonants can be arranged in 5! = 120 ways.
Total arrangement = 720 ways( 120*6).

9. There are 2 red balls, 5 orange and 4 purple balls .Two balls are drawn at random.What is the probability that one is red the other is orange or purple?
12/55
11/55
16/55
18/55
17/55
Option D
There are 2 red balls and 9 other color balls. So total balls= 11
2 balls drawn at random,
=> required probablity= 2C1 * 9C1/11C2
=2*9/11*10/2
=>36/110 =18/55

10. There are 8 students are selected from dance school for dance competition.The total number of students are 18.
In how many ways can be the selection be made so that 2 students are always included?
8008
5005
6006
7007
9009
Option A
If 2 members are always included
The total number of ways= 2C2 * 16 C 2
=8008