Yid intended to type a seven-digit number, but the two 3's he meant to type did not appear. What appeared instead was the five-digit number 52115. How many different seven-digit numbers could Yid have meant to type?  Choose the correct choice from the following answers.
A) 10
B) 16
C) 21
D) 24
E) 27
Yid intended to type a seven-digit number Should be 21.   there are two possibilities for placing 2 3s .   case 1: two 3s were missed consecutively. i.e. he typed 33 and it came blank on screen.   -5-2-1-1-5- in this arrangement we can fit 33 in 6 ways . (Six dashes, each dash represent one possible place for placing 33)   case 2: two 3s are not together, i.e. they have one or more digits between them .   -5-2-1-1-5- , in this arrangement   if we place first 3 at first dash i.e. 35-2-1-1-5- then the other 3 can fit into 5 places.   if we place first 3 at second dash i.e. -532-1-1-5- then the other 3 can fit into 4 places.   if we place first 3 at third dash i.e. -5-231-1-5- then the other 3 can fit into 3 places.   if we place first 3 at fourth dash i.e. -5-2-131-5- then the other 3 can fit into 2 places.   if we place first 3 at Fifth dash i.e. -5-2-1-135- then the other 3 can fit into 1 place.   so total 15 ways.   case 2 + case 1 = 6+ 15= 
<gadget id="calculator">6+ 15</gadget>
<output>21</output>
21 ways   Answer 21
<result>C</result>
Yid intended to type a seven-digit number, but the two 3's he meant to type did not appear. What appeared instead was the five-digit number 52115. How many different seven-digit numbers could Yid have meant to type?