## Question

Ten persons, amongst whom are *A, B *and *C* are to speak at function. Find number of ways in which it can be done if *A* wants to speak before B, and*B* wants to speak before *C*?

### Solution

We will follow the steps as shown:

**Step I : **Select three places for *A, B* and *C* to speak in ^{10}C_{3} ways.

**Step II : **Arrange *A, B, C* on selected seats in 1 way.

**Step III : **Arrange remaining 7 persons in 7! Ways.

Total no. of ways = (^{10}C_{3} × 1) × 7!

#### SIMILAR QUESTIONS

How many integral solutions are there to *x* + *y* +* z* + *t *= 29, when *x **≥* 1, y*≥ *2, *z* *≥ *3* *and *t* *≥ *0?

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*x*_{1} + *x*_{2} + *x*_{3} + *x*_{4} + *x*_{5} = 20 and *x*_{1} + *x*_{2} + *x*_{3} = 5 when *x*_{k} ≥ 0?

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