问题1.评估。
我)8！
解决方案：
8! = 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1
= 56 × 30 × 12 × 2
= 1680 × 24
= 40320
ii)4！ – 3！
解决方案：
4! -3! = 4 × 3! – 3!
= 3! × (4 – 1)
= 3! × 3
= 6 × 3
= 18
问题2。是3！ + 4！ = 7！ ?
解决方案：
L.H.S = 3! + 4!
= 3! + 4 * 3!
= 3! * (1 + 4)
= 3! * 5
= 60
R.H.S = 7!
= 7 × 6 × 5 × 4 × 3 × 2 × 1
= 42 × 20 × 6
= 42 × 120
= 5040
As l.H.S ≠ R.H.S
NO, 3!+ 4! is not equal to 7!
问题3.计算8！/(6！ × 2！)
解决方案：
8!/(6! × 2!)
= 8 × 7 × 6 ! / (6 ! × 2!)
Now, both 6! on numerator and denominator will be cancelled
= 8 × 7/2 × 1
= 4 × 7
= 28
问题4.如果(1/6！)+(1/7！)=(y / 8！)，则求y。
解决方案：
L.C.M of 6! and 7! is 7!
We can write the equation like this,
(7 + 1)/7! = (y/8!)
8 × 8!/7 ! = y
8 × 8 × 7! / 7! = y
8 × 8 = y
y = 64
Hence, value of y is 64
问题5.评估n！/(n – r)！什么时候
i)n = 6，r = 2
解决方案：
n!/(n – r)!
Here n = 6 and r = 2, we have
6!/(6 – 2)!
= 6!/4!
= 6 × 5 × 4!/4!
= 6 × 5
= 30
ii)n = 9，r = 5
解决方案：
n!/(n – r)!
Here n = 9 and r = 5, we have
9!/(9 – 5)!
= 9!/4!
= 9 × 8 × 7 × 6 × 5 × 4!/4!
= 9 × 8 ×7 × 6 × 5
= 72 × 7 × 30
= 72 × 210
= 15120