How many numbers of five digits can be formed by using 1, 2, 3, 4, 5, if 4 is necessarily taken at h

M4maths Previous Puzzles

31 May 2014 Solve

How many numbers of five digits can be formed by using 1, 2, 3, 4, 5, if 4 is necessarily taken at hundred's place and 2 is not allowed at unit's place. Repetition of numbers is not allowed.

OPtion

1) 72
2) 16
3) 12
4) 120
5) 96
6) 24
7) 60
8) 30
9) 18
10)None of these

Solution

4 is necessarily taken at hundred's place and 2 is not allowed at unit's place,
hence number of methods = 1*3*3*2*1 = 18
You can also check the answer by making different numbers under given conditions.

Option 9)

Correct Option: 9 Best Solution (7)

Udhaya kumar   10 years AGO

4 fac - 3 fac = 18....

Like? Yes (6) | No (3)  

Ramsb   10 years AGO

4 is hundred place is 1 way

2 is not in unit's place that can be placed in remaning 3 places is 3 ways

remaning 3 places can be placed is 3*2*1=6 ways...
total is 1*3*3*2*1=18 ways....

Like? Yes (4) | No (1)  

sngupta   10 years AGO

3*2*1*1*3=18
hundred\'s place=1 option (4)
unit\'s place=3 option (any of 1,3,5)
remaining place\'s have 3,2,1 option respectively.

Like? Yes (4) | No (1)  

Saraswathy   10 years AGO

Numbers starting with 2 is 3! ( 2_4_ _)
Numbers having 2 in 1000th digit is 3! (_24_ _)
Numbers having 2 in 10's digit is 3! (_ _ 4 2 _)
Totally 3! + 3! + 3! = 18 ways

Ans : 18 (Option 9)

Like? Yes (4) | No (2)  

susmit   10 years AGO

Only one way for 4.
3 Ways for 2.
3 factorial ways for remaining three digits.
So, 1*3*3! = 18

Like? Yes (3) | No (2)  

Divya Singhal   10 years AGO

let there are b 5 seats...
_ _ _4 _ _
4 comes at hundered's place..n 2 cannot comes at unit place..so possibility are as follows from frst place to last..
1*2*1*3*3=18

Like? Yes (1) | No   

candy   10 years AGO

at units place 2 is not allowed and 4 is placed at hundred's place.
so at units place possibility will be !3.
at tens place possibility will again be !3 (because 4 and the other number which will be placed at units place will not be allowed.)
then at hundred's place 4 is placed as mentioned in the ques so possibilty will be !1.
then at thousand's place possibility will be !2
and only one didgit will left for ten thousand's place.
on multiplying...
!1*!2*!1*!3*!3 = 18

Like? Yes (1) | No