Agroup of five friends go to a restaurant for dinner. the restaurant offers 20 different main dishes. (a) suppose that the group collectively orders five different dishes to share. the waiter just needs to place all five dishes in the center of the table. how many different possible orders are there for the group? (b) suppose that each individual orders a main course. the waiter must remember who ordered which dish as part of the order. it's possible for more than one person to order the same dish. how many different possible orders are there for the group? (c) suppose that each individual orders a main course. the waiter must remember who ordered which dish as part of the order. however the friends agree that no two people will order the same dish.

In δabc shown below, ∠bac is congruent to ∠bca: triangle abc, where angles a and c are congruent given: base ∠bac and ∠acb are congruent. prove: δabc is an isosceles triangle. when completed (fill in the blanks), the following paragraph proves that line segment ab is congruent to line segment bc making δabc an isosceles triangle. (4 points) construct a perpendicular bisector from point b to line segment ac . label the point of intersection between this perpendicular bisector and line segment ac as point d: m∠bda and m∠bdc is 90° by the definition of a perpendicular bisector. ∠bda is congruent to ∠bdc by the definition of congruent angles. line segment ad is congruent to line segment dc by by the definition of a perpendicular bisector. δbad is congruent to δbcd by the line segment ab is congruent to line segment bc because consequently, δabc is isosceles by definition of an isosceles triangle. 1. corresponding parts of congruent triangles are congruent (cpctc) 2. the definition of a perpendicular bisector 1. the definition of a perpendicular bisector 2. the definition of congruent angles 1. the definition of congruent angles 2. the definition of a perpendicular bisector 1. angle-side-angle (asa) postulate 2. corresponding parts of congruent triangles are congruent (cpctc)