Exercises 10-13. (Ordering n objects) 10. In how many different ways can 9 objec

Question

Exercises 10-13. (Ordering n objects) 10. In how many different ways can 9 objects be ordered? inhow many different ways can 5 children be scated at 5 desks? In how many different ways can 5 different colored flags be hoisted on a mast? 13. In how many different ways can 10 pig eons roost in 10 pigeon holes, if pigeons like to sleep alone? Exercises 14-17. (Picking r objects from n when order counts) In how many different ways can 10 pigeons roost in 15 pigeon holes, if pigeons like to sleep alone? 14. 15. In how many different ways can 5 children be seated at 11 desks? 16. In how many different ways can 5 of 11 children be seated at 5 desks? 17. In how many different ways can 5 of 7 different colored flags be hoisted on a mast?

Explanation / Answer

12 ) as here order matters ; therefore from top to bottom there are 5 places where a flag can be hoisted

for 1 st place there are 5 choice ; for 2nd there are 4 choice as one flag has been put for 1st place ; for 3rd place 3 ; for fourth 2 and for fifth 1 choice

hence number of ways =5! =5*4*3*2*1=120

16)

as first we need to pick 5 children out of 11 and then put them in order to sit in desk; therefore

number of ways =11P5 =11!/(11-5)! =11!/6! =11*10*9*8*7=55440

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