Question

How many 3 digit even numbers can be formed from 1,3,4,7 an 8 with no repetition?

Answer 1

1) 114

2)134

3)144

4)174

5) 184

6)314

7) 334

8) 344

9)374

10) 384

11) 414

12) 434

13) 444

14) 474

15)484

16) 714

17) 734

18) 744

19) 784

20) 774

21) 814

22) 834

23) 844

24)874

25) 884

into 2

total=50

Answer 2

$Among\ 1,\ 3,\ 4,\ 7\ and\ 8,\ two\ are\ even\ \to\ 4\ \&\ 8 \\ \\ Let's\ find\ the\ no.\ of\ 3-digit\ numbers\ whose\ ones\ digit\ is\ 4. \\ \\ \bold{4}\ numbers\ have\ been\ hundreds\ digit\ \to\ 1,\ 3,\ 7\ and\ 8 \\ \\ As\ repetition\ is\ not\ allowed,\ \bold{3}\ numbers\ have\ been\ tens\ digit\ \\ \to\ Three\ among\ 1,\ 3,\ 7\ and\ 8 \\ \\ Only\ \bold{1}\ number\ has\ been\ ones\ digit\ \to\ 4 \\ \\ 4 \times 3 \times 1 = \bold{12}$

$\\ \\ \therefore\ \bold{12}\ numbers\ can\ be\ formed\ with\ ones\ digit\ 4. \\ \\ The\ same\ in\ the\ case\ of\ numbers\ with\ ones\ digit\ 8. \\ \\ I.\ e.,\ \bold{12}\ numbers\ can\ be\ formed\ with\ ones\ digit\ 8. \\ \\ Add\ both. \\ \\ 12 + 12 = \bold{24} \\ \\ \therefore\ \bold{\underline{\underline{24}}}\ numbers\ can\ be\ formed. \\ \\ And\ that\ numbers\ are:$

$134,\ \ \ \ \ 174,\ \ \ \ \ 184,\ \ \ \ \ 314,\ \ \ \ \ 374,\ \ \ \ \ 384, \\ \\ 714,\ \ \ \ \ 734,\ \ \ \ \ 784,\ \ \ \ \ 814,\ \ \ \ \ 834,\ \ \ \ \ 874,\_\_\_ \\ \\ 138,\ \ \ \ \ 148,\ \ \ \ \ 178,\ \ \ \ \ 318,\ \ \ \ \ 348,\ \ \ \ \ 378, \\ \\ 418,\ \ \ \ \ 438,\ \ \ \ \ 478,\ \ \ \ \ 718,\ \ \ \ \ 738,\ \ \ \ \ 748,\_\_\_$

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