Statement I The number of ways of distributing 10 identical balls in 4 distinct boxes such that no box is…
Statement I The number of ways of distributing 10 identical balls in 4 distinct boxes such that no box is empty is ${ }^9 C_3$.
Statement II The number of ways of choosing 3 places from 9 different places is ${ }^9 \mathrm{C}_3$.
Statement I is true, statement II is true, statement II is not a correct explanation for statement I
Statement I is true, statement II is false
Statement I is false, statement II is true
Statement I is true, statement II is true, statement II is a correct explanation for statement I
Solution
Statement I The number of ways of distributing 10 identical balls in 4 distinct boxes such that no box is empty is ${ }^9 C_3$.
$\because n$ identical things can be distributed to different boxes by ${ }^{t-1} C_{r-1}$ ways such that no box is empty.
10 identical balls can be distributed to 4 distinct boxes by ${ }^{10-1} C_{4-1}$ ways
i.e. ${ }^9 C_3$ ways
Statement II The number of ways of choosing 3 places from 9 different places is ${ }^9 C_3$ (true)
$\therefore$ Statement I is true statement II is true, statement II is not a correct explanation for statement I.