In how many ways Ram can distributed $40$ identical apples to his six children named $A, B, C, D, E$ and $F$ such that $A$ gets two more than $B, C$ gets $3$ more than $F$ and $D$ gets five less then $E$ and any one gets at least on fruit

^{14} C_{2}

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^{14} C_{12}

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1001

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91

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Solution

The correct option is A $^{14} C_{2}$
Total apples $= 40$
we know that
$A = B + 2$
$C = F + 3$
$D = E - 5$
so,
$B + 2 + B + F + 3 + D + D + 5 + F = 40$
$2 F + 2 B + 2 D = 30$
$F + B + D S = 15$
No. of ways of distributing $n$ identical objects into $r$ persons
so, that no one is empty handed $^{n - 1} C_{r - 1}$
solutions: $(^{14} C_{2})$

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In how many ways Ram can distributed 40 identical apples to his six children named A,B,C,D,E and F such that A gets two more than B,C gets 3 more than F and D gets five less then E and any one gets at least on fruit

The correct option is A 14C2Total apples =40we know that A=B+2C=F+3D=E−5so,B+2+B+F+3+D+D+5+F=402F+2B+2D=30F+B+DS=15No. of ways of distributing n identical objects into r personsso, that no one is empty handed n−1Cr−1 solutions: (14C2)

In how many ways Ram can distributed $40$ identical apples to his six children named $A, B, C, D, E$ and $F$ such that $A$ gets two more than $B, C$ gets $3$ more than $F$ and $D$ gets five less then $E$ and any one gets at least on fruit