Question

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 1

21 ways

Explanation:

number = 7 digit

5 digit no = 52115

to find out

How many different seven-digit numbers

solution

first we need to place the two missing 3s in the number 52115

we consider here two cases

case 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 ways

If 3 and 3 are together so there = 6 ways

= 15 + 6 = 21 ways