Question

(c) (5 points) How many even 5-digit numbers are there for which no digit is 0, and the digit 6 appears exactly once? For instance, 55634 and 16118 are such numbers, but not 63304 (has a 0), nor 63364 (too many 67s), nor 55637 (not even).

Answer 1

arranged in number this, '6' can be I! 101 Til ol ! II o I'll 5- digit 5 ways. Toll 1 no 1 1 1 E 3 ES IM @

Lets take 1st Possibility of 6. 8 possibilities 6 T Here Except Possibilities Here (0,6) only 2, 4, 8 can come. remaining 8 numbers can come. so, & ways I 8 8 8 3 = 3483 ways Lets take and possibility of 6. I sways 6 sways sways 3 ways 2 8 XIX 8 X 8 X 3 = 3483 ways, similarly for 3rd and 4th possibility of 6 have 3x8² ways each. 5th possibility of 6 sways sways & wars & wars 6 8 x 8 x 8 x 8 x1 = 84 ways.

total no of required 5 digit numbers = 3X 83 + 3x 83 + 3x8?+ 3x8?+ fx 83 = 204.83 ways..