A panel for a political forum is made up of 13 people from three parties, all seated in a row. The panel consists of 4 Socialists, 1 Republican, and 8 Green Party members. In how many distinct orders can they be seated if two people of the same party are considered identical (not distinct)?

A sales assistant is hanging 13 sweaters on a rack. He has 3 white sweaters, 4 black sweaters, and 6 purple sweaters. In how many distinct orders can the sweaters be arranged if two sweaters of the same color are considered identical (not distinct)?

Answer the questions below.(If necessary, consult a list of formulas.)(a) There are 16 appetizers available at a restaurant. From these, Abdul is to choose 12 for his party. How many groups of 12 appetizers are possible?(b) A certain committee consists of 16 people. From the committee, a president, a vice-president, and a treasurer are to be chosen. In how many ways can these 3 office

Twelve People are sitting in two parallel rows containing six People each, in such a way that there is equal distance between adjacent persons. In row-I B, C, D, E, F and G are seated and all of them are facing south. In row-2 P, Q, R, S, T and U are seated and all of them are facing north. Therefore, in the given seating arrangement, each member seated in a row faces another member of the other row. (Please note: None of the information given in necessarily in the same order). R sits second to the right of S. Only one person sits between R and U. C sits to the immediate left of the one who faces U. Only two people sit between C and F. Q sits fourth to the left of T. G is an immediate neighbour of the one who faces T. D does not face R. B sits third to the right of D. E is an immediate right of B. G does not face P.Who amongst the following is facing C?QRPU

A committee of six is chosen from 14 people. In how many ways can this be done?

Isabel is arranging 11 cans of food in a row on a shelf. She has 7 cans of carrots, 3 cans of beans, and 1 can of beets. In how many distinct orders can the cans be arranged if two cans of the same food are considered identical (not distinct)?