Sid 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 Sid have meant to type?

Answer:21 ways Step-by-step explanation:number = 7 digit5 digit no = 52115to find out How many different seven-digit numberssolutionfirst we need to place the two missing 3s in the number 52115we consider here two casescase 1  the two 3's appear separated (like 532135 or 3521135)  case 2 the two 3's appear together (like 5332115 or 5211533)  Case 1 we can see  that number type as _5_2_1_1_5_  place 3's placeholders show potential locations( type a ) for  3's  separated we will select 2 of  6 place and place 3 in every location so we do this 6C2  = (15) ways  and (type b): again use same step as  _5_2_1_1_5_  here 3s together for criterion and we will select 1 of the 6 place and place both 3s here and there are 6 ways.  so that here will be 15+6=21 ways If 3 and 3 are separate so 6C2 = 15  waysIf 3 and 3 are together so there = 6  ways= 15 + 6 = 21 ways