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

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26 Jul 2021 Combination

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) 18
5) 96
6) 24
7) 60
8) 30
9) 15
10) None of the above

Solution

Keeping 4 fixed at 100th position.
so there are 4 digits left.
Out of which 2 can not be placed in units place.
permutation of units place is 3.
permutation of 10000th place is 3
permutation of 1000th place is 2 .
permutation of 100 place is 1
permutation of 10th place = 1
So total permutation - 3 X 2 X 3 X 1 X 1= 18

Correct Option: 4 Best Solution (2)

SAYAN CHATTERJEE   3 years AGO

keeping 4 in hundred's place varieties are 4!= 24
and also keeping 2 in unit's place the varieties are 3!= 6
so, reqd is (24-6)= 18.
Option 4.

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G.S.Kantharao   3 years AGO

No.of digits=5
Hundred's place fixed with 4
Number of 5 figured =4*3*2*1=24
Now number of figures with 2 in units place=3*2*1=6
So,number of 5 figured numbers which contains 4 in hundreds not 2 in units =24-6=18
My option is 4 👈

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