(B) To select $r$ items from $n$ items in a row such that no two are consecutive,the formula is given by $^{n-r+1}C_r$. Here,$n = 10$ and $r = 4$. Sub

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(B) To select $r$ items from $n$ items in a row such that no two are consecutive,the formula is given by $^{n-r+1}C_r$. Here,$n = 10$ and $r = 4$. Substituting the values,we get $^{10-4+1}C_4 = ^7C_4$. Since $^7C_4 = ^7C_3$,we calculate: $^7C_3 = \frac{7 \times 6 \times 5}{3 \times 2 \times 1} = 35$.

Class 11 Mathematics Permutations and Combinations Definition of combinations, Condition combinations

There are $10$ points in a row. In how many ways can $4$ points be selected such that no two of them are consecutive?

A
$140$
B
$35$
C
$104$
D
None

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Permutations and Combinations

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Definition of combinations, Condition combinations

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There are $10$ points in a row. In how many ways can $4$ points be selected such that no two of them are consecutive?

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