(C) Given,total questions in part $A = 6$ and total questions in part $B = 7$. To choose $10$ questions with at least $4$ from each part,the possible

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(C) Given,total questions in part $A = 6$ and total questions in part $B = 7$. To choose $10$ questions with at least $4$ from each part,the possible combinations are: $1$. $4$ from part $A$ and $6$ from part $B$ $2$. $5$ from part $A$ and $5$ from part $B$ $3$. $6$ from part $A$ and $4$ from part $B$ Total ways = $({ }^{6}C_{4} \times { }^{7}C_{6}) + ({ }^{6}C_{5} \times { }^{7}C_{5}) + ({ }^{6}C_{6} \times { }^{7}C_{4})$ $= (15 \times 7) + (6 \times 21) + (1 \times 35)$ $= 105 + 126 + 35 = 266$

Class 11 Mathematics Permutation and Combination Definition of combinations, Condition combinations

Easy

$A$ student has to answer $10$ questions,choosing at least $4$ from each of the parts $A$ and $B$. If there are $6$ questions in part $A$ and $7$ in part $B$,then the number of ways the student can choose $10$ questions is:

KCET 2021 All KCET

A
$256$
B
$352$
C
$266$
D
$426$

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Permutation and Combination

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Definition of combinations, Condition combinations

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$A$ student has to answer $10$ questions,choosing at least $4$ from each of the parts $A$ and $B$. If there are $6$ questions in part $A$ and $7$ in part $B$,then the number of ways the student can choose $10$ questions is:

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