Question

4 triangle box, 6 rectangle box, 3 square box, 8 books

i) How many way can we stack all the item in to single stack?

ii) we want single stack but we don't care about the order of triangle box and rectangle box. But we do care the order of square box and books. In this situation, how many way can we stack all the item in single stack?

iii) How many way we can stack all the item in single stack that all each type of item are together?

Please explain detail and correctly. Thanks

Answer 1

Here we have 4- bon - triangle 6-rectangle boul 3-square 8 books bou Total 4+6+348 =121 in when each triangle we 1 Square a put in single stack bon will be identical Similarly rectangle boxs bor and books. So this is the Similar problem of making string of length 20 where Letter repeated 4-times 8 second letter repeated 6-times third 3. times I fourth letter repeated 8- temes. SO total number of possible stacks 21! 4. 6! 318! 9 letter repeated 1

☺ don't Here order as we Care about of triangle bon and rectanglar bose So these things will be treated identical to each other. But care about square box and books these things will be treated unique Hence Number of Possible stack is we Hence these as box and only need to 21! divide for triangle 4! 6! rectangle bon. of item (10) As is like is need we to make stack for four different things not for alo four things can be put in stack in each type together so it our So 4), ways а 24