Answer 1 only determine who will give a gift to whom. Inhow many ways can this be done if exactlyfour staff members draw their own name?1. Consider arranging flags along the length ofa flagpole. Rectangular flags come in sixdifferent colors and triangular flags come intwo colors (different from the colors of therectangular flags). The top flag must betriangular. In how many different ways canthree to five flags be arranged on the polea. if repetition of colors is allowed?b. if repetition of colors is not allowed?2. In how many ways can twenty 1000-pesobills be given away to four of ten peoplewhere each of the four receives at least one5. A sports store sells tennis racquets of sixdifferent brands: Wilson, Prince, Babolat,Dunlop, Yonex and Head. In how many wayscan you purchase four racquets so that youpurchase must include a Wilson or a Princetennis racquet?6. Define a recurrence relation and allnecessary initial conditions for the followingproblem:A string of n Christmas lights are to becreated using green, red and clear bulbs. Inhow many ways can this be done so that notwo clear bulbs are next to each other?1000-peso bill?3. Ten national leaders are to be seated at around table at a summit. If the presidents ofthe US and Russia do not wish to be seatednext to each other, in how many ways canthis be done?7. Solve the recurrence relation A, = 4 A2-3.An-1 subject to the initial conditions A, = 5and A, = 10.4. The 25 staff members of an office decide tohold a Kris Kringle to celebrate the holidaysand draw names written on slips of paper to

“Since you have asked multiple question, we will solve the first question as you mentioned. If you…

1. Consider arranging flags along the length of a flagpole. Rectangular flags come in six different colors and triangular flags come in two colors (different from the colors of the rectangular flags). The top flag must be triangular. In how many different ways can three to five flags be arranged on the pole a. if repetition of colors is allowed? b. if repetition of colors is not allowed?