Question

In a certain algebraical exercise book there are $4$ examples on arithmetical progressions, $5$ examples on permutation-combination and $6$ examples on binomial theorem. Number of ways a teacher can select for his pupil atleast one but not more than $2$ examples from each of these sets, is_________.

Answer 1

Number of way teacher can select examples from arithmetic progression $={}^4{C}_1+{}^4{C}_2$

No. of ways the teacher can select examples from permutation -combination ${}^5{C}_1+{}^5{C}_2$

No: of ways the teacher can select examples from binomial theorem $={}^6{C}_1+{}^6{C}_2$

$\therefore$ Total no: of ways $={(}^4{C}_1{+}^4{C}_2\left){(}^5{C}_1{+}^5{C}_2\right){(}^6{C}_1{+}^6{C}_2)=10\times 15\times 21=3150$