How many ways are there to choose 10 items from 6 distinct items when a) the items in the choices are ordered and repetition is not allowed? b) the items in the choices are ordered and repetition is allowed? c) the items in the choices are unordered and repetition is not allowed? d) the items in the choices are unordered and repetition is allowed?

Answer: a) 151200, b) 1000000, c) 210, d) 5005.Step-by-step explanation:Since we have given thatNumber of items = 10Number of distinct items = 6a) the items in the choices are ordered and repetition is not allowed?[tex]^{10}P_6\\\\=151200[/tex]b) the items in the choices are ordered and repetition is allowed? [tex]10^6\\\\=1000000[/tex]c) the items in the choices are unordered and repetition is not allowed? [tex]^{10}C_6\\\\=210[/tex]d) the items in the choices are unordered and repetition is allowed?[tex]^{15}C_6=5005[/tex]Hence, a) 151200, b) 1000000, c) 210, d) 5005.