In how many ways can the letters in Saskatchewan be rearranged and still maintain the order in which the vowels appear?
My guess: 12!/2!3!(4!/3!) because the vowels aaea can only have four total arrangements.
Your guess is partially correct! To find the number of ways the letters in Saskatchewan can be rearranged while maintaining the order of the vowels, we will break down the problem into different parts:
1. Count the number of permutations of the consonants: In Saskatchewan, we have eight letters in total, of which four are consonants (S, S, K, T, C, H, W, N). The number of ways to arrange these consonants is given by 8!/2!2! (dividing by 2! twice because of the repeated S's).
2. Count the number of arrangements of the vowels: In Saskatchewan, we have four vowels (A, A, E, A). However, as you correctly pointed out, the vowels (A, A, E, A) can only be arranged in four distinct orders, since the two A's are indistinguishable. Therefore, the number of ways to arrange the vowels is 4!/2!, where we divide by 2! because of the repeated A's.
3. Multiply the number of possibilities: To find the number of total arrangements, we multiply the number of consonant arrangements by the number of vowel arrangements: (8!/2!2!) * (4!/2!).
Therefore, the correct answer is (8!/2!2!) * (4!/2!). Evaluating this value gives us the final answer for the number of ways to rearrange the letters while maintaining the order of the vowels in Saskatchewan.