Nine cards are numbered 1, 2, 2, 3, 3, 4, 6, 6, 6.Three of the nine cards are chosen and placed in a line, making a 3-digit number. Find how

Question

many different numbers can be made in this way if the number is between 200 and 300.

Tell me answer in terms of permutation and combinations.

Answer 1

The first digit is 2
That leaves 5 unique digits (12346) to choose from, giving 5P2 = 20
But you have to add the 2 numbers with repeated digits: 233 and 266
total: 22 choices

Answer 2

We have 5 digits that are unique in which we have to chose from. We need to get two digits from five to get (5P2) numbers to be formed. We have two digits that are repeated in the range that is 6 and 3. and so we must add 2P2. in total we will have a total of 5P2+2P2 numbers formed. This sums to 22 numbers.