(C) The set of digits is $\{1, 2, 3, 4, 5, 6, 7\}$.Odd digits are $\{1, 3, 5, 7\}$ (total $4$) and even digits are $\{2, 4, 6\}$ (total $3$).We need t

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(C) The set of digits is $\{1, 2, 3, 4, 5, 6, 7\}$.Odd digits are $\{1, 3, 5, 7\}$ (total $4$) and even digits are $\{2, 4, 6\}$ (total $3$).We need to select $2$ odd digits from $4$ and $2$ even digits from $3$.Number of ways to select the digits $= {}^{4}C_{2} \times {}^{3}C_{2} = 6 \times 3 = 18$.These $4$ selected digits can be arranged in $4!$ ways.Total number of $4$-digit numbers $= 18 \times 4! = 18 \times 24 = 432$.

Class 11 Mathematics Permutation and Combination Definition of combinations, Condition combinations

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The number of $4$-digit numbers without repetition that can be formed using the digits $1, 2, 3, 4, 5, 6, 7$ in which each number has two odd digits and two even digits is:

KCET 2019 All KCET

A
$436$
B
$454$
C
$432$
D
$450$

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Definition of combinations, Condition combinations

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The number of $4$-digit numbers without repetition that can be formed using the digits $1, 2, 3, 4, 5, 6, 7$ in which each number has two odd digits and two even digits is:

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The domain of definition of the function $f(x) = \log_{[x + \frac{1}{x}]} |x^2 - x - 6| + ^{16-x}C_{2x-1} + ^{20-3x}P_{2x-5}$ is,where $[x]$ denotes the greatest integer function.

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