If the number of function from the set A - 0-1-2 and B- 0-1-2-3-4-5-6-7 such that fi- fj-i- j-i-j- A20 k - then the value of k is

Number of function such that f(0) lt; f(1) lt; f(2)= ^8C_3 Number of function such that f(0)= f(1) lt; f(2)= ^8C_2 Number of function such tha ...

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Standard XII

Mathematics

Combination

If the number...

Question

If the number of function from the set $A = {0, 1, 2}$ and $B = {0, 1, 2, 3, 4, 5, 6, 7}$ such that $f (i), \leq f (j), i < j; i, j ϵ A 20 k$ , then the value of $k$ is

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Solution

Number of function such that $f (0) < f (1) < f (2) =^{8} C_{3}$
Number of function such that $f (0) = f (1) < f (2) =^{8} C_{2}$
Number of function such that $f (0) < f (1) = f (2) =^{8} C_{2}$
Number of function such that $f (0) = f (1) = f (2) =^{8} C_{1}$
$∴$ required number of function
$=^{8} C_{3} +^{8} C_{2} +^{8} C_{2} +^{8} C_{1}$
$=^{9} C_{3} +^{9} C_{2} +^{10} C_{3} = 120$

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If the number of function from the set A={0,1,2} and B={0,1,2,3,4,5,6,7} such that f(i),≤f(j),i<j;i,jϵA20k , then the value of k is

Number of function such that f(0)<f(1)<f(2)=8C3Number of function such that f(0)=f(1)<f(2)=8C2Number of function such that f(0)<f(1)=f(2)=8C2Number of function such that f(0)=f(1)=f(2)=8C1∴ required number of function =8C3+8C2+8C2+8C1=9C3+9C2+10C3=120

If the number of function from the set $A = {0, 1, 2}$ and $B = {0, 1, 2, 3, 4, 5, 6, 7}$ such that $f (i), \leq f (j), i < j; i, j ϵ A 20 k$ , then the value of $k$ is