Mathematics - Permutation & Combination Question with Solution | TestHub

MathematicsPermutation & CombinationArrangement under ConstraintHard2 minPYQ_2021

MathematicsHardsingle choice

The number of seven digit integers with sum of the digits equal to $10$ and formed by using the digits $1, 2$ and $3$ only is:

Answer:

Solution:

$(I)$ First possiblity is $1, 1, 1, 1, 1, 2, 3$

required number $= \frac{7!}{5!} = 7 \times 6 = 42$

$(II)$ Second possiblity is $1, 1, 1, 1, 2, 2, 2$

required number $= \frac{7!}{4! 3!} = \frac{7 \times 6 \times 5}{6} = 35$

Total $= 42 + 35 = 77$

Stream:JEESubject:MathematicsTopic:Permutation & CombinationSubtopic:Arrangement under Constraint

⏱ 2mℹ️ Source: PYQ_2021

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