Which of the following gives the number of ways to make a 3-digit locker combination out of the digets 0-9 if the numbers are not repeated

720

Step-by-step explanation:

The total digits in 0-9 are 10. To make a 3-digit locker combination, the digits should not be repeated.

There are 10 digits so any number out of 10 can be put in the first place of the combination.

So, ans=10

Now suppose 7 comes at first place and therefore (10-1) = 9 digits are remaining to be put at the second place.

So, ans=10*9

Assume 5 comes at the second place in the combination and therefore (9-1) = 8 digits are remaining to be put at the third place.

So, ans=10*9*8=720

312312

step-by-step explanation:

∠1≅∠2 by the alternate exterior angles theorem.

step-by-step explanation:

given, a ∥ b and ∠1 ≅ ∠3 .we have to prove that e ∥ f

we know that ∠1≅∠3 and that a || b because they are given. we see that by the alternate exterior angles theorem. therefore, ∠2≅∠3 by the transitive property. so, we can conclude that e || f by the converse alternate exterior angles theorem.

we have to fill the missing statement.

transitivity property states that if a = b and b = c, then a = c.

now, given ∠1≅∠3 and by transitivity property ∠2≅∠3 .

hence, to apply transitivity property one angle must be common which is not in result after applying this property which is ∠1.

the only options in which ∠1 is present are ∠1 and ∠2, ∠1 and ∠4

∠1 and ∠4 is not possible ∵ after applying transitivity we didn't get ∠4.

hence, the missing statement is ∠1≅∠2.

so, ∠1≅∠2 by the alternate exterior angles theorem.