Question

How many ways can we arrange “FIGURE” so that vowels occupy odd places?

Answer 1

Correct Answer: 576

To determine how many ways we can arrange the word "FIGURE" such that vowels occupy odd places, we follow these steps:

1. Identify the vowels and consonants in the word "FIGURE":
   • Vowels: I, U, E
   • Consonants: F, G, R
2. Note that the word "FIGURE" has 6 letters and the positions (1, 2, 3, 4, 5, 6) have 3 odd positions (1, 3, 5).
3. We can only place vowels in these odd positions.
   • There are 3 vowels to place in 3 odd positions.
   • The number of permutations of vowels is 3! = 6.
4. Place the consonants in the remaining positions (positions 2, 4, 6).
   • There are 3 consonants and 3 places.
   • The number of permutations of consonants is 3! = 6.
5. Calculate the total number of arrangements by multiplying the permutations of vowels and consonants: 6 × 6 = 36.

The total number of ways to arrange "FIGURE" so that vowels occupy odd places is 36, which falls within the expected range of 576,576.