probability question

The steps are listed below. You can easily use your HKEA Approved Calculator to find the answers, as I do not have the Calculator on hand ( I am in a restaurant using WiFi to connect online ):


(a) P( 1 graphical designer )

= ( 7C6 x 8C1 ) / 15C7 .....


(b) P( Each type at least one member )

= P( 1, 1, 5 ) + P( 1, 2, 4 ) + P( 1, 3, 3 ) + P( 1, 4, 2 ) + P( 1, 5, 1 ) + P( 2, 1, 4 ) + P( 2, 2, 3 ) + P( 2, 3, 2 ) + P( 2, 4, 1 )

= [ ( 2C1 x 5C1 x 8C5 ) + ( 2C1 x 5C2 x 8C4 ) + ..... + ( 2C2 x 5C4 x 8C1 ) ] / 15C7 ....


Note: Listing in this method is even faster than considering its Complementary Event


(c) P( Odd no. of each type )

= P( 1, 1, 5 ) + P( 1, 3, 3 ) + P( 1, 5, 1 )

= [ ( 2C1 x 5C1 x 8C5 ) + ( 2C1 x 5C3 x 8C3 ) + ( 2C1 x 5C5 x 8C1 ) ] / 15C7 ....


Hope I can help you.

http://img412.imageshack.us/img412/8679/95647773.png