Question 1153845

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An English teacher needs to pick {{{10}}} books:
 
{{{4}}} novels,   
{{{8}}} plays,   
{{{5}}} poetry books, and 
{{{5}}} nonfiction books 
-----------------
total: {{{22}}} books


number of ways to choose {{{10}}} from {{{22}}}

= {{{C(22,10)=646646}}}

what can't we have:

if she wants to include no more than {{{3}}} novels, we have

= {{{C(4,3)*C(19,3)}}}  

deduct of the number of ways = {{{C(22,10) - C(4,3)*C(19,3) }}}

= {{{646646 - 4*969}}}
= {{{642770}}}
or in scientific: {{{6.43*10^5 }}}