How many distinct (identical-looking) arrangements (permutations) of the word PROBABILITY are there if: (A) There are no restrictions other than the one discussed in lecture that the two 'B's look the same and the two 'I's look the same? (B) The arrangement must begin with a vowel and end in a consonant. (C) If you do not change the order of the vowels or consonants, that is, the arrangement must look like this: ...A...I...I...0... # the ... represent 0 or more consonants if you only look at the vowels, and the same arrangement must look like this ...P...R...B...B...L...T...Y... # the ... represent 0 or more vowels if you only look at the consonants. (D) The arrangement contains the substring BABY , that is, it looks like this: ...BABY... How many distinct (identical-looking) arrangements (permutations) of the word PROBABILITY are there if: (A) There are no restrictions other than the one discussed in lecture that the two 'B's look the same and the two 'I's look the same? (B) The arrangement must begin with a vowel and end in a consonant. (C) If you do not change the order of the vowels or consonants, that is, the arrangement must look like this: ...A...I...I...0... # the ... represent 0 or more consonants if you only look at the vowels, and the same arrangement must look like this ...P...R...B...B...L...T...Y... # the ... represent 0 or more vowels if you only look at the consonants. (D) The arrangement contains the substring BABY , that is, it looks like this: ...BABY