"First you have to count the number of times that each letter" "occurs. We have 2 MAT and 1 HEICS. Then we have to use"
"the multinomial distribution : "
"number of arrangements = "(11!)/((2!)^3 (1!)^5) = 4989600
"(i) The vowels are AAEI and they have to be together. We"
"have 4!/2! = 12 possible arrangements in the vowels, and 8"
"possible placements of the vowels series, and "(7!)/((2!)^2) =
"1260 possible arrangements of the consonants. Multiplying"
"the three together, we get 12 * 8 * 1260 = 120960."
"(ii) If the two T are together, they can be in 10 possible positions"
"or placements. For the other letters, there are "(9!)/((2!)^2) =
"90720 possibilities, so in total 907200 possibilities for the two"
"T together, so if they cannot be together we have"
"4989600 - 907200 = 4082400 possibilities."
