Question

EVALUATE EACH OF THE FOLLOWING. LEAVE ANSWER IN REDUCED FRACTION FORM. DO NOT LEAVE ANSWER IN DECIMAL FORM.A) _6C6_8C0 = __________B) 10C3 = __________C) _9P5_10C4 = __________D) _6C2_6P2 = __________E) _7P0_7C0 = _________

Answer 1

Solution A) = 1

Analysis:

`(_6C_6)/(_8C_0)=((6!)/(6!(6-6)!))/((8!)/(0!(8-0)!))`

We know for rules of combinations 0!=1

`(_(6)C_(6))/(_(8)C_(0))=((6!)/(6!(6-6)!))/((8!)/(0!(8-0)!))=((720)/(720\ast1))/((40320)/(1\ast40320))=(1)/(1)=1`

Solution B): 120

Analysis

`_(10)C_3=(10!)/(3!(10-3)!)=(3628800)/(6\ast5040)=(3628800)/(30240)=120`

Solution C)=72

Analysis

`(_9P_5)/(_(10)C_4)=((9!)/((9-5)!))/((10!)/(4!(10-4)!))=((362880)/(24))/((3628800)/(17280))=(15120)/(210)=72`

Solution D)=1/2

Analysis:

`(_6C_2)/(_6P_2)=((6!)/(2!(6-2)!))/((6!)/((6-2)!))=((720)/(48))/((720)/(24))=(15)/(30)=(1)/(2)`

Solution E)=1

Analysis

`(_7P_0)/(_7C_0)=((7!)/((7-0)!))/((7!)/(0!(7-0)!))=1`