[SPM Add Math Permutation and Combination]

[Far]

The answer for this question is 1701100 but I got 1701000 for my first step. The question state that the digit cannot be repeated so for box number 2 there is a chance that the number chosen is either consonant or vowel so I think there are 2 ways and I sum both ways but I got different answer …How to solve this question ya?

[D.B]

Question

44. (a) Rajah menunjukkan satu kata laluan yang perlu ditetapkan oleh Najwa pada Instagramnya.
    Diagram shows a password that needs to be set by Najwa on her Instagram.

Kata laluan Instagram terdiri daripada 2 huruf kecil, diikuti oleh nombor 3 digit dan diikuti 1 huruf besar. Najwa ingin membuat kata laluan dengan syarat huruf kecil pertama bukan huruf vokal, nombor pertama tidak boleh 0 dan huruf besar mestilah huruf vokal. Berapa banyak kata laluan yang boleh dibuat jika pengulangan tidak dibenarkan?
The Instagram password consists of 2 lower case letters, followed by 3 digit numbers, and followed by 1 upper case letter. Najwa wants to create password with the condition that the first case lefter cannot be a vowel, the first number cannot be 0 and the upper case letter must be a vowel. How many passwords can be created if repetitions are not allowed?
[4 markah / marks]

Answer

Hi Farhaini,
Sorry for the rather late reply, I was quite uncertain due to the wording of the question. I believe the question is a bit ambiguous, because by saying “repetitions not allowed”: is using “a” then “A” count as a repetition or not? Since we repeatedly used the letter “a” twice, but one is a lower case and the other is an upper case.

Assuming that using “a” then “A” doesn’t count as a repetition because of the upper and lower case scenario, then your first working is correct.

Assuming that using “a” then “A” counts as a repetition because we used the letter “a” twice, then the approach would be different. We have to consider two separate cases:

1. the second letter is a vowel (a, e, i, o, u) - which would mean that we only have 4 choices for the upper-case vowel since we used one vowel previously.
2. the second letter is a consonant - which would mean that we have 5 choices for the upper-case vowel since we didn’t use a vowel previously.

So the working would be like this:

But since the answer in the first scenario is closer to the mark scheme answer, it’s most likely your working is correct and there is a typing error in the mark scheme.

Hope this helps!

[Far]

Thank you very much!