Question

2) How many different 6-digit numbers can be formed from the digits 4, 5, 2,1, 8,9?/ अंकों 4, 5, 2, 1, 8,9 से कितने
6-अंकों वाली संख्याएं निर्मित की जा सकती हैं।
1.480
2.360
3.720
4.840​

Answer 1

Step-by-step explanation:

3, 1, 7, 0, 9, 5, i.e. 6 digits.

The total numbers of 6 digit numbers

6! - 5! = 720-120 = 600.

(i) 5! = 120 having 0 at the end.

(ii) Divisible by 5.

They will have zero in the last place and hence the remaining 5 can be arranged in 5! = 120 ways.

They may have 5 in the last place and as above we will have 5! = 120 ways. These' will also include numbers which will have zero in the first place. Therefore the numbers having zero in 1st and 5 in last place will be 4!

Therefore 6 digit numbers having 5 in the end will be

5! -4! = 120 - 2.4 = 96.

Therefore the total number of 6 digit numbers divisible by 5 is

120 + 96 = 216.

(iii) Not divisible by 5.

= Total - (divisible by 5)

=600 - 216 = 384.