Kenneth Rosen: Counting-Chapter 5

Question

How many license plates consisting of three letters followed by three digits contain no letter or digit twice?

Comments

Considering possibel letter set as english alphabet (small or capital but not both = 26 letters) and digits (0,1,...9)

We can have 26*25*24*10*9*8 = 11232000

Answer 1

So, every letter and digit must be unique.

$26 \times 25 \times 24 \times 10 \times 9 \times 8$

Comments

Yes Sir answer is correct
but i thought that is the possible answer when qstn is NO letter and NO digit twice
it says OR

so suppose ABC112 doesnt count here ? No letter twice or no digit twice
Inclusion Exclusion principle. Is it not applicable here ?

---

Nopes. That is the ambiguity of English language. We have to apply the common meaning as per English.

contain no letter or digit twice

means no 2 letters allowed AND no 2 digits allowed. We should parse the sentence as

• contain no ((letter or digit) twice)
• contain no (letter twice or digit twice)
• contain no letter twice and contain no digit twice

When negation comes inside, AND/OR are reversed - DeMorgan's principle. This is applied in many questions.

---

yes got it.sir . Doubt cleared :)

---

Sir, what if the mean only twice (but, we can have thrice)?
What will be the answer in that case?