the-sum-of-the-four-digit-even-numbers-that-can-be-formed-with-digits-0-3-5-4-without-repitation-

Question Number 39846 by vajpaithegrate@gmail.com last updated on 12/Jul/18

the sum of the four digit even numbers that can be formed with digits 0 3 5 4 without repitation

Commented by Rasheed.Sindhi last updated on 13/Jul/18

43536

Commented by vajpaithegrate@gmail.com last updated on 13/Jul/18

how sir pls explain

Answered by Rasheed.Sindhi last updated on 13/Jul/18

∵ The numbers are even

∴ The unit place can be filled with 0 or 4

Case : - - - 0

When unit is 0

tens can be filled in 3 ways (3, 4 or 5)

after that hundreds can be filled in 2 ways

and thousands can be filled in 1 way only .

∴ Total numbers with unit 0 :

1 \times 3 \times 2 \times 1 = 6

Case : - - - 4

When unit is 4

thousands can be filled in 2 ways (3 or 5)

(It {can}^{'} t be 0 as in that case the numbers

will be of 3 digits)

hundres can be filled in 2 ways and

tens can be filled in 1 way .

∴ Total numbers with unit 4 :

1 \times 2 \times 2 \times 1 = 4

So sum of units of all the 10 numbers is

0 \times 6 + 4 \times 4 = 16 (6 units & 1 carry to tens .

Case : - - 0 -

When tens is 0 \to unit can be filled in 1 way (with 4)

\to hundreds can be filled in 2 ways (3 or 5)

\to thousands can be filled in 1 way .

∴ Total numbers with tens 0

1 \times 1 \times 2 \times 1 = 2

Case : - - 4 -

1 \times 1 \times 2 \times 1 = 2

Case : - - 3 -

2 \times 1 \times

Continue

Answered by Rasheed.Sindhi last updated on 13/Jul/18

5430 + 4530 + 5340 + 3540 + 4350

+ 3450 + 5304 + 3504 + 5034 + 3054

= 43536

Note : The numbers have been achieved

by tree - diagram, which {can}^{'} t be drawn

by forum - keyboard .