On the refrigerator, mathematics is spelled out with $11$ magnets, one letter per magnet. two vowels and four consonants fall off and are put away in a bag. if the t's, m's, and a's are indistinguishable, how many distinct possible collections of letters could be put in the bag
Non extraneous information (Information that matters): - Mathematics has 11 letters - The bag must contain 4 vowels and 2 consonants - t's, m's, and a's are indistinguishable ——— Bag Combinations Step 1: List all: aeaimt aeaimh aeaimm aeaimc aeaims aeaith aeaitt aeaitc aeaits aeaihc aeaihs aeaics ——— Bag Combinations Step 2: Change all t's, m's, and a's to another variable so they are indistinguishable (k) : kekikk kekikh kekikk kekikc kekiks kekikh kekikk kekitc kekiks kekihc kekihs kekics ——— Bag Combinations Step 3: Remove doubles and list: kekikk kekikh kekikc kekiks kekitc kekihc kekihs kekics
