11 persons are made to sit in a row, then number of ways of selecting of 4 persons such that no two of them are consecutive is
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Answer:
Let P
1
,P
2
,P
3
,P
4
,P
5
,P
6
,P
7
,P
8
,P
9
,P
10
be the persons sitting in this order.
If three are selected (non consecutive) tnen 7 are left out.
Let P,P,P,P,P,P,P be the left out & q,q,q be the selected. The number of ways in which these 3 q's can be placed into the 8 positions between the P's (including extremes) is the number ways of required selection.
Thus number of ways=
8
C
3
=56.
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