Let \(A = \{1, 2, 3, 4, 5, 6, 7\}\). The number of surjective functions defined from \(A\) to \(A\) such that \(f(i) = i\) for at least four values of \(i\) from \(i = 1, 2, \ldots, 7\) is:
Match the following lists and choose the correct code.List IList IIa. Four dice (six faced) are rolled. The number of possible outcomes in which at least one dice shows 2 isp. 210b. Let \(A\) be the set of 4-digit number \(a_1 a_2 a_3 a_4\), where \(a_1 > a_2 > a_3 > a_4\). Then \(n(A)\) is equal toq. 480c. The total number of three-digit numbers, the sum of whose digits is even, is equal tor. 671d. The number of four-digit numbers that can be formed from the digits 0, 1, 2, 3, 4, 5, 6, 7 so that each number contains digit 1 iss. 450Codes:abcd(1)qspr(2)srqp(3)rpsq(4)psqr
If the 11 letters \(A, B, \ldots, K\) denote an arbitrary permutation of the integers \((1, 2, \ldots, 11)\), then \((A-1)(B-2)(C-3)\cdots(K-11)\) will be
If the total number of strictly increasing functions defined from $f : \{1,2,3,4,5,6\} \to \{1,2,3,...,9\}$ is $k$ then $\frac{k}{12}$ is equal to _______
Number of six digit numbers that can be formed using digits 1, 2, 3, 4, 5, 6 (each digit used exactly once) having the property that for each digit, not more than two digits smaller than that digit appear to the right of that digit, is:
Let $N$ be the number of four digit even numbers such that if 3 is one of the digits, then 5 is the succeeding digit. If $N = P_1^\alpha P_2^\beta P_3^\gamma$ ($P_1,P_2,P_3$ are primes, $\alpha,\beta,\gamma\in\mathbb{N}$), then $P_1+P_2+P_3$ is