Permutaion and Combination

1. Five boys and three girls are about to form a queue
( i ) If the boys are not going to stand in both ends, how many
ways for form such a queue?
( ii ) If the boys must stand next to one another, how many
ways to form such a queue?
Sol:
( i )
3 個女孩人選 2 人站在頭尾兩端
方法有 P32 種
剩餘的 1 個女孩和 5 個男孩排列方式有 6! 種
所有的排列方式
P32 × 6!
＝ 6 × 720
＝ 4320
( ii )
將 5 個男孩視同 1 人, 和 3 個女孩共 4 人
排列方式有 4! 種
5 個男孩的排列方式有 5! 種
所有的排列方式共有
4! × 5!
＝ 24 × 120
＝ 2880
Ans: ( i ) 4320 ways ( 2 ) 2880 ways
2. How many different ways to select three prefects from a
group of 9 students?
Sol:
C93 ＝ (9*8*7)/(3*2*1) ＝ 84
Ans: 84 ways
3. How many different ways to select a captain and a vice captain
from a group of 13 students?
Sol:
P132 ＝ 13 × 12 ＝ 156
Ans: 156 ways

1. ( i ) 4320 ways ( 2 ) 2880 ways

2. 84 ways

3. 156 ways