Hi there I have a question...

Can anyone explain me this question which is along with its answer!

Count the set S of 3 digit numbers which begin or end

with an even digit.

Assume that 0 is even but a number cannot begin with 0.

The set is the union of the two subsets:

• The set B of three digit numbers that begin

with 2, 4, 6 or 8.

This set has cardinality

(4)(10)(10).

(why?)

• The set C of three digit numbers that end with

0, 2, 4, 6, or 8 and do not begin with 0.

This set has cardinality

(5)(9)(10). <<How come here it is (5)(9)(10) instead of (5)(10)(10)?

(why?)

• Now we use the inclusion-exclusion principle

to eliminate the overlap of sets B and C.

Their intersection:

The 3 digit numbers that begin with 2, 4, 6, or 8 and end

with 0, 2, 4, 6, or 8.

The intersection has the cardinality

(4)(10)(5)

Hence the cardinality is

400 + 450 - 200 = 650.

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