Q.1 In how many ways can you send 5 children to 7 classroom :
I) When there is no restriction ?
A) 16807 ways
B) 2401 ways
C) 117649 ways
D) 343 ways
Ans. A
Ist child can go in any 7 classroom
2nd child can go in any 7 classroom
3rd child also in any 7 classrooms
Therefore, 7*7*7*7*7 = 16807 ways
II) Such that two children are in the same class ?
A) 2520 ways
B) 5040 ways
C) 840 ways
D) 740
Ans. A
1st children in 7 classes
2nd children in 6 classes
3rd in 5 classes
4th in 4 classes
5th children in 3 classes
Therefore, 7*6*5*4*3 = 2520 ways
III) Such that atleast two children are in the same class ?
A) 14287
B) 2639
C) 116809
D) 397
Ans. A
This you can easily calculate just by subtracting above two i.e. all the ways – ways in which restriction is there
Therefore, 16807 – 2520 = 14287 ways
Q.2 How many number of 5 digits can be formed with the digits 0,1,4,5,6,7 & 8 ?
A) 2160 ways
B) 1800 ways
C) 2220 ways
D) 1440 ways
Ans. A
At first place of 5 digit nos., we can’t put 0
So, 6P1 = 6
And, for remaining 4 digits we are left with 6 digits, then
6P4 = 6*5*4*3
= 360
Therefore number of ways = 360*6 = 2160
Q.3 How many words can be formed out of the letters of the word ARTICLE so that the vowels occupy even places ?
A) 144 ways
B) 120 ways
C) 168 ways
D) None of the above
Ans. A
There are 3 vowels & can be placed at 3 even places = 3p3 = 3*2*1 = 6 ways
There are 4 consonants which can be put in 4 places.
Then, 4P4 = 24 ways
Or 24*6=144 ways
Q.4 In how many ways can 8 children sit on 8 seats number A,B,C,D,E,F,G,H ?
I) With no restriction
A) 40320 ways
B) 6720 ways
C) 20160 ways
D) None of the above
Ans. A
8*7*6*5*4*3*2*1 = 40320 ways
(Write in this way keeping in mind 1st child can sit at 8 seats)
II) such that 8 children can sit on 8 seats such that Ramesh sits on seat C ?
A) 7!
B) 8!
C) 6!
D) 9!
Ans. A
Since Seat C is fixed then it can be arranged in 7! ways
III) Such that Ramesh is just left of Suresh ?
A) 7!
B) 6!
C) 8!
D) 5!
Ans. A
(1 + 6!)
Q.5 Ranjit likes to take a different route to work each day. He always walks alongside part of the park & only ever travels south or east.
In the diagram lines represent streets in this area.
How many different routes are there by which Ranjit can walk from home to the Work ?
H
PARK
w
A) 4
B) 3
C) 6
D) 8
Ans. C
When he will go downwards then ways can be d d d (3 times downward)
After then when he will go right then ways will be R R R (3 times right)
Therefore, 6 Will be answer
If it has asked to find the no. of ways then,
You should apply in this way 6! / 3! 3!
