2. Of the three-digit integers greater than 700, how many have two digits equal to each other and the remaining digit different? A) 90 B) 82 C) 80 D) 45 E) 36

correct option is C) 80

Step-by-step explanation:

given data

three-digit integer > 700

solution

As we know that 3 digit number can be here as 3 patterns

1. all 3 digit distinct

2. 2 a like and 3rd is different

3. all 3 digit are a like

so here

we get here (2.) 2 a like and 3rd is different

that is Total - (1) - (3)

here total 3 digit number greater than 700 as 700 to 999

total = 299

when all 3 digit distinct, 1st digit have only 3 values they are 7, 8, 9

so they will as

all 3 digit distinct = 3 * 9 * 8

all 3 digit distinct = 216

and

when all 3 alike they are

all 3 alike = 3

as they is 777, 888 and 999

so that two digits equal to each other and the remaining digit different is

= 299 - 216 - 3

=80

so correct option is C) 80