Question

in how many ways can at least two team members be selected for grade a out of 7 members in a group

Answer 1

Any odd degree polynomial with real coefficients has at least one real root. In what follows, I ..... Oops - nice answer to the wrong question. 1 .... So necessary conditions are.

Answer 2

Answer:   120

Step-by-step explanation:

We know that the number of ways to select r things from n things is given by :_

$^nC_r=\dfrac{n!}{(n-r)!}$

Then, the number if ways to select at least two team members  out of 7 members in a group :-

$^7C_2+^7C_3+^7C_4+^7C_5+^7C_6+^7C_7$         (1)

Since, $^nC_0=^nC_n=1$ and $^nC_1=^nC_{n-1}=n$

Therefore, (1) becomes

$\dfrac{7!}{2!(7-2)!}+\dfrac{7!}{3!(7-3)!}+\dfrac{7!}{4!(7-4)!}+\dfrac{7!}{5!(7-5)!}+7+1\\\\=\dfrac{7!}{2!(5)!}+\dfrac{7!}{3!(4)!}+\dfrac{7!}{4!(3)!}+\dfrac{7!}{5!(2)!}+8\\\\=21+35+35+21+8=120$

Hence, the number if ways to select at least two team members  out of 7 members in a group =120