Question

Let A be the set of five-digit numbers abcde, where a > b > c > d > e. If number of elements in A is k, then the value of k/4 is

Answer 1

Answer:

ok ,

Step-by-step explanation:

a=C−2D

b=C−D

c=C

d=C+D

e=C+2D

Then,

a+b+c+d+e=5C=α

3

....(i)

b+c+d=3C=β

2

......(ii)

From (i) and (ii)

5

α

3

=

3

β

2

For this least possibility is

α=5×3,β=5×3×3

α=15,β=45

C=

5

α

3

=

5

15

3

=675

c=C=675

hope it helps

thank you ✌☺

Answer 2

Answer: 63

Step-by-step explanation:

The set A of all five-digit numbers (abcde)_10 with a > b > c > d > e, is in one-to-one correspondence with the set of all 5-element subsets of the 10-set.

S = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}, because having chosen any subset of S with five distinct elements, we can arrange it in a strictly increasing order uniquely.

A has exactly C (10,5) = 10×9×8×7×$\frac{6}{5!}$ = 252 elements.

Hence, k=|A| = 252.

Therefore, $\frac{k}{4} =\frac{252}{4}$ = 63.

#SPJ3