Draw a circle C on a plane. put n distinct pointson the circumference of C.Join any two of the n points with a chord. Suppose that no three chords intersect at any one point inside C. Let Cn be the number of such chords , in that of intersections of the chords inside C ,and rn that of regions in C bounded by and arc and/or some chords .Answer the following questions below.
(1) Find C1 , C2 , C3 , C4 , C5 , C6
(2) Find i1 ,i2 , i3 , i4 , i5 , i6
(3) Find r1 , r2 , r3 , r4 , r5 , r6
(4) Express Cn , in , rn with binomial coefficients interms of n.
(For binomial coefficients (m k ) ,note that (m k)=0 if m<k )
คณิตทุนญี่ปุ่น: ช่วยแปล และ หาคำตอบให้ดูทีครับ งงนิดหน่อย กลัวจะเข้าใจผิดครับ.
(1) Find C1 , C2 , C3 , C4 , C5 , C6
(2) Find i1 ,i2 , i3 , i4 , i5 , i6
(3) Find r1 , r2 , r3 , r4 , r5 , r6
(4) Express Cn , in , rn with binomial coefficients interms of n.
(For binomial coefficients (m k ) ,note that (m k)=0 if m<k )