#"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."#
