<PRE><B>Question 1173585</B>
.
Kate wants to choose 3 out 13 different items as the christmas presents. 
Given that 4 items are from shop B, and 3 items from shop C, 
find the number of combinations in each of the following cases.

A. Choosing 3 items from the same shop.
B. Choosing 3 items which are not from shop A
C. Choosing at least 1 item from shop A
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&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;In the post by &amp;nbsp;@ewatrrr, &amp;nbsp;part &amp;nbsp;(A) &amp;nbsp;and part&amp;nbsp;(B) &amp;nbsp;answered correctly, &amp;nbsp;but part &amp;nbsp;(C) &amp;nbsp;answered &amp;nbsp;INCORRECTLY.


&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;I came to bring the correct solution to part &amp;nbsp;(C).



&lt;pre&gt;
So we have a pool of  13 items, in all;

    6 of them are from shop A;   4 are from shop B   and   3 are from shop C.


(C).  Find the number of combinations, given that at least 1 item is from shop A.


      Then we have THESE 3 possible cases


          1 item is from A:     {{{C[6]^1*C[7]^2}}} = 6*21 = 126 combinations


          2 items are from A:   {{{C[6]^2*C[7]^1}}} = 15*7 = 105 combinations

          
          3 items are from A:   {{{C[6]^3}}} = 20 combinations.


     The total of these cases is  {{{C[6]^1*C[7]^2}}} + {{{C[6]^2*C[7]^1}}} + {{{C[6]^3}}} = 126 + 105 + 20 = 251.   &lt;U&gt;ANSWER for part (C)&lt;/U&gt;
&lt;/pre&gt;

Solved.



. . . . . . . . 


@ewatrrr fixed her post after seeing my solution.



</PRE>