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  • In how many ways can a collection of one or more foot-wears be displayed from 16 cone heels, 5 platform heels, 6 kitten heels and 9 high heels?Option:

In how many ways can a collection of one or more foot-wears be displayed from 16 cone heels, 5 platform heels, 6 kitten heels and 9 high heels?

Option: 1

7610


Option: 2

7410


Option: 3

7139


Option: 4

7140


Answers (1)

Note the following:

  • The formula for the combination for the selection of the \mathrm{x} items from the \mathrm{y}different items is \mathrm{=^{y}C_{x}=\frac{y!}{x!\left ( y-x \right )!}}

  • The combination for the selection of the none or more items from the \mathrm{n}identical items is \mathrm{=n+1}

From the available data, the following is evident.

  • The combination for the selection of the none or more cone heels is =16+1=17

  • The combination for the selection of the none or more platform heels is =5+1=6

  • The combination for the selection of the none or more kitten heels is=6+1=7

  • The combination for the selection of the none or more high heels is=9+1=10

Therefore, the required combination is

=17\times6\times7\times10-1

=7139

 

 

 

Posted by

Kshitij

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