Question for Hung Woei Neoh

Probability Level 2

HUNG WOEI NEOH \large \text{HUNG WOEI NEOH}

From the name above, how many different names (including the above one) can be created such that the relative order of consonants and vowels does not change.

Details and Assumptions:

  • "The relative order of consonants and vowels does not change" means that vowels and consonants should occupy the same places as they did in the original name, but they can be juggled with their places.
  • An example would be "GEHW NIOO HEUN".


The answer is 32400.

Ashish Menon by Ashish Menon , 20, India

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1 solution

Ashish Menon
May 14, 2016

Vowels occupy the second, sixth, seventh, eight, tenth and eleventh places. There are 6 vowels in which O and E repeat twice. So, they can be arranged in 6 ! 2 ! × 2 ! = 180 \dfrac{6!}{2! × 2!} = 180 ways. Consonants occupy the first, third, fourth, fifth, ninth and twelfth places. There are six consonants in which H and N repeat twice. So, they can be arranged in 6 ! 2 ! × 2 ! = 180 \dfrac{6!}{2! × 2!} = 180 ways. So, the total number of words that can be formed with the given name such that the relative order of the consonants and vowels do not change = 180 × 180 = 32400 180 × 180 = \boxed{32400} .

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