Please answer a AND b, with explanations. Do not post incomplete, I will thumbs

Question

Please answer a AND b, with explanations. Do not post incomplete, I will thumbs down. Thank you.

work committee should inelude 4 people from hendquarters and 5 people fron regional oflices. There are 10 people at hendquarters who are K to be on the committee, and 15 people from regional offices who are willing. (a) IHow many committees can be formed? (b) Suppose that one of the headquarters candidates is the mother of a daughter among the regional candidates. It is decided that these two should not serve on the same committee. How many committees can be formed now?

Explanation / Answer

a) No. of commitees = No. of ways of selecting 4 from 10 in headquarters * No. of way of selecting 5 from 15 in regional = 10C4 * 15C5 = 10*9*8*7 * 15*14*13*12*11 / [1*2*3*4*1*2*3*4*5]= 630630

b) If mother is selected, daughter can't be selected no . of way = 9C3 * 14C5 = 9*8*7/6 * 14*13*12*11*10/120=168168

If daugther is selected, no. of way = 9C4 * 14C4 = 9*8*7*6 / 24 * 14*13*12*11/24 = 126126

If both are not selected , no. of ways = 9C4 * 14C5 = 9*8*7*6 / 24* 14*13*12*11*10/120 = 252252

Total = 168168+126126+252252 = 546546

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