Question

1) How many ways can six books be arranged on one shelf? a) 21 b) 120 c) 360 d) 720 2) There are eight girls competing in an ice-skating competition. In how many ways can they finish in first, second, and third place? a) 336 b) 1,680 c) 2,016 d) 40,320 3)How many ways can a president and vice president be selected from a class of 12? a) 23 b) 72 c) 132. d) 1,320 4)How many ways can seven students line up for a class picture? a) 5,040 b) 210 c) 28 d) 7

Answer 1

Answer: The correct options are

(d) 720.

(a) 336.

(c) 132.

(a) 5040.

Step-by-step explanation: The calculations are as follows:

(1) The number of ways in which six books be arranged on one shelf is given by

`6!=6*5*4*3*2*1=720.`

So, the total number of ways is 720.

Option (d) is CORRECT.

(2) Given that there are 8 girls competing in an ice-skating competition.

So, the number of ways in which they can finish in first, second, and third place is given by

`8* 7* 6=336.`

Thus, the total number of ways is 336.

Option (a) is CORRECT.

(3) The number of ways in which a president and vice president can be selected from a class of 12 is given by

`12*11=132.`

Thus, the total number of ways is 132.

Option (c) is CORRECT.

(4) The number of ways in which 7 students can line up for a class picture is given by

`7!=7*6*5*4*3*2*1=5040.`

Thus, the required number of ways is 5040.

Option (a) is CORRECT.

Answer 2

1 ) 6 · 5 · 4 · 3 · 2 · 1 = 720
Answer: D ) 720
2 ) 8 · 7 · 6 = 336
Answer: A ) 336
3 ) 12 · 11 = 132
Answer: C ) 132
4 ) 7 · 6 · 5 · 4 · 3 · 2 · 1 = 5,040
Answer: A ) 5,040