This is a binomial distribution type problem where the probability under the question is the sum


     P =       (1)


The number of trials is              10;
The indexes of success trials        k = 6,7,8,9,10
The probability of success trial     p = 0.6;
                                     q = 1 - p
C(n,k) = n! / (k! * (n-k)!)          are binomial coefficients.


The sum  (1)  is equal to  1 - .     (2)



Instead of calculating every term of (2) manually and then summing them up, you may use Excel function 

BINOM.DIST(5, 10, 0.6, TRUE)  to calculate the value


     = 0.366897.    


Therefore, the value of  (2)  is equal to  1 - 0.366897 = 0.633103 (approximately).    ANSWER