M4maths Previous Puzzles

22 Jan 2016 How many number

If repetition of numbers is not allowed then 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.

OPtion

1) 72
2) 16
3) 12
4) 120
5) 96
6) 18
7) 60
8) 30
9) 15
10)24

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 6)

Correct Option: 6 Best Solution (19)

sugayathri   9 years AGO

3 no's are placed in 3! ways=6

4 is placed in 1 way
2 is placed in 3 ways
=6*1*3=18

Like? Yes (3) | No   

BONAM SRINIVAS   9 years AGO

first 4 is placed in hundred's place in 1 way,next 2 should not in units place so remaining 3 no. placed in 3 ways,now remaining 3 places,here repetition not allowed
10's place is filled in 3 ways now remaining 2 places is filled in 2 ways and last 1 way
therefore total ways=1*3*3*2*1=18 ways

Like? Yes (2) | No   

Vishwadeep Solpankhi   9 years AGO

out of 5 digits, 4 is fixed for hundredths place. remaining 4 digits which are 1,2,3,5 for remaining 4 places.
So, hundredth place can be filled in only 1 way (4)
Digit 2 is not allowed at units place.
so Units place can be filled in 3 ways (1,3,5 (because repetition is not allowed) )
Tens place can now be filled in 3 ways (digit 4 is used for hundredth place and any one digit except 2 is used for units place, so we are left with 3 digits as 2 have been used)
Now, thousands place can be filled in 2 ways
ten thousands place can be filled in 1 way

Answer = No. of ways = 3x3x1x2x1 = 18

Like? Yes (2) | No   

suryakant singh   9 years AGO

4 is fix then we have only 1,2,3,5
2 is not allowed at unit place then
at unit place we have 3 option ...similarly at 10 place we have 3 option then
at next place 2 and then 1 so,we can form 3*3*2*1 numbers means 18

Like? Yes (1) | No   

Yashi Das   9 years AGO

4 in hundred's place ->1way
2 not to be in unit's place -> 3 ways
remaining 3 places can be filled by -> 3*2*1=6ways
therefore,
1*3*3*2*1=18 ways

Like? Yes (2) | No (1)  

neeraja   9 years AGO

1 as 1st digit ----- 4 nos
2 as 1st digit ----- 6 nos
3 as 1st digit ----- 4 nos
5 as 1st digit ----- 4 nos
total 18 nos

Like? Yes (1) | No   

Abhikant Bhave   9 years AGO

3 at units place 3at
tens place 1 at hundreds place 2 at thousand place 1 at ten thousand place
so 3 � 3� 1�2�1

Like? Yes (1) | No   

Digvijay singh tomar   9 years AGO

Since 4 Is fixed at 100th postion.
therefore possibility of putting 4 At 100th place is 1 .

now 2 Can't be placed at unit position.
therefore possibility for unit's position is 3,
i.e. 1,3,5 Can come at unit's place.
now remaining three numbers are put at remaining positions without repitition.
therefore

3*3*1*2*1=18

Like? Yes (1) | No   

vipin pandey   9 years AGO

as hundred place can be filled in only 1 way and unit place can be filled in 3 ways and remaining by 3�2�1

Like? Yes (1) | No   

S VANI   9 years AGO

hundred's place is replaced with only 4.
then unit's place is not replaced with 2 then possible chances for filling unit's digit is 3(remaining no's).
ten's place filled with remaining digits i.e., 3.
thousand's place filled with 2 digits.
tenthousand's place filled with remaining 1 digit.
finally answer =(1*2*1*3*3)=18.

Like? Yes (1) | No   

Parag Wagh   9 years AGO

For no. 4 = 1 place
for 2 = 3 places
for 3 = 3 places
for 5 = 2 places
for 1 = 1 place
total = 1*3*3*2*1 = 18

Like? Yes (1) | No   

sumit kumar   9 years AGO

we call fill hundred's place with 1 way.....(1)
unit place 2 is not allowed so it can be filled with 3 possible way....(2)
repetition is nort allowed so ten's place can fill with 3 ways...(3)
4th place can filled with 2 position way....(4)
5th place can filled with 1 possible way.....(5)
with equation (1) to (5)
total possible way to form a number is 1*2*1*3*3=18
option 6

Like? Yes (1) | No   

RITESH KUMAR JHA   9 years AGO

keeping 4 at hundred place by 1 way, with ought keeping 2 at unit place. it will 3 way. after that 3 way again by keeping 2 . now by 2 way and last by 1 way again. and at last ans is from unt place to last place= 3�3�1�2�1=18

Like? Yes (1) | No   

Jaydev Dinda   9 years AGO

As per question, 4 has to be at hundred place..
Case 1
if 4 is hundred place and 2 is at unit place then possible arrangements of 5 digit number are 3!*1*1=6
Case 2
If 4 is at hundred place then possible arrangements of 5 digit number are 4!=24.

Hence, 4 at hundred place and 2 is not unit place,
24-6=18
Option 6 (ans)

Like? Yes (1) | No   

v.sudha   9 years AGO

no. of ways of filling 4 in the hundred places=1
remaining 4 numbers in the units place except 2=3
remaining 3 numbers in the tens place =3
2 numbers in thousand place=2
last position=1
total no. of ways=1*2*3*3*1=18 ways

Like? Yes (1) | No   

v.pravalika   9 years AGO

4 in hundred position =1
except 2 remaining 3 digits in units place=3
including 2 tens place=3
thousand place=2
last position=1
total no.=18

Like? Yes (1) | No   

Shyam Sundar   9 years AGO

4 has been decided so we have 4 places to put on .
on unit digit 2 can't come so there is possibility of using 3 no.s 1,3,5 so for 3 ways and for tens we'll have again three including 2 but one no. has been put in unit place .
So for it 3 ways and so for thousand place 2 and ten thousands place 1 .
1*2*3*3

Like? Yes (1) | No   

Rajani Chaganti   9 years AGO

4 is fixed..so it can be arranged in one way
2 should not be arranged in units place.so it can be arranged in 3 ways..
then remaining numbers are arranged in 3! ways..so
1�3�6=18 ways

Like? Yes (1) | No   

Saleel Kulkarni   9 years AGO

possible nos at hundred's place =1
at unit's place = 3 as no 2 is not allowed
at ten's place = 3
at thousand = 2
at ten thousand = 1
1*3*3*2*1=18

Option 6)

Like? Yes (1) | No