In how many ways can 6 persons be selected fr | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(C) The total number of ways to select $6$ persons from $12$ (i.e.,$4$ officers + $8$ constables) is given by $^{12}C_6$.The number of ways to select

Vedclass · Accepted Answer

$896$

Vedclass · Answer

(C) The total number of ways to select $6$ persons from $12$ (i.e.,$4$ officers + $8$ constables) is given by $^{12}C_6$.The number of ways to select $6$ persons such that no officer is included (i.e.,all $6$ are selected from $8$ constables) is $^8C_6$.According to the condition,at least one officer must be included. Therefore,the required number of ways is:Total ways - Ways with no officers = $^{12}C_6 - ^8C_6$.Calculating the values:$^{12}C_6 = \frac{12 	imes 11 	imes 10 	imes 9 	imes 8 	imes 7}{6 	imes 5 	imes 4 	imes 3 	imes 2 	imes 1} = 924$.$^8C_6 = ^8C_2 = \frac{8 	imes 7}{2 	imes 1} = 28$.Required ways = $924 - 28 = 896$.

In how many ways can $6$ persons be selected from $4$ officers and $8$ constables,if at least one officer is to be included?

Similar Questions

The number of four-digit numbers strictly greater than $4321$ that can be formed using the digits $0, 1, 2, 3, 4, 5$ (repetition of digits is allowed) is

In how many different ways can the letters of the word '$BANKING$' be arranged so that the vowels always come together?

If all the words,with or without meaning,are written using the letters of the word $QUEEN$ and are arranged as in an English dictionary,then the position of the word $QUEEN$ is (in $^{th}$)

If $x, y$ and $r$ are positive integers, then $^x{C_r} + ^x{C_{r-1}} \cdot ^y{C_1} + ^x{C_{r-2}} \cdot ^y{C_2} + \dots + ^y{C_r} = $

The value of $\sum\limits_{r = 1}^{15} {{r^2}\,\left( {\frac{{^{15}{C_r}}}{{^{15}{C_{r - 1}}}}} \right)} $ is equal to

Vedclass Test Series

Exam Paper Generator

Online Exam Module